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Resource allocation in multiuser multicarrier cognitive radio network via game and supermarket game theory: survey, tutorial, and open research directions.

1. Introduction

Recent studies by the Federal Communication Commission (FCC) have shown that the conventional fixed spectrum allocation approach is becoming insufficient for addressing today's rapidly developing wireless communications, and there is a call for open spectrum access [1]. To meet this drastic demand in wireless spectrum, dynamic spectrum access (DSA) and cognitive radio (CR) were introduced as intelligent approaches/techniques to solve the problems associated with the fixed spectrum approach and have received significant interest from researchers (see [2] for a comprehensive review). Cognitive radio (also referred to as secondary user (SU) or unlicensed user) can be defined as a technique in which wireless devices have the ability to sense and discover a specific range in the frequency spectrum to identify currently unused bands (also called spectrum holes) for transmission purposes without interfering with the owner of the spectrum (also referred to as primary user (PU) or licensed user).

One of the most commonly occurring problems when addressing CRNs is allocation of the available resources (e.g., power and subcarrier) to CRs. This is because both PUs and CRs occupy the same spectrum band and transmit independently. Thus, CRs require flexible PHY to allow dynamic reconfiguration of the transmitted power and the signal frequency. One of the most promising candidates that can provide proper flexibility and high performance in CRN is the multicarrier technique [3].

Game theory is a mathematical tool that can be used to model scenarios in which the actions of decision makers, also called players, are in conflict. In CRNs, CR nodes attempt to access the licensed band, which belong to PUs, for their transmission purposes. Thus, the interaction among two decision makers (i.e., CRs and PUs) takes place, and game theory is shown to be an effective tool for analyzing and modeling resource allocation in such a scenario. The setup of spectrum allocation in CRNs is quite similar to the interaction of people in a real market, where the owner of the spectrum can 'rent' the temporary vacant band to CRs for their needs. This simple scenario makes adopting market theory as a game an interesting tool in modeling the problem of resource allocation in CRNs.

In this article, we have followed a simple strategy to introduce readers to the concept of (i) CRNs, (ii) game theory, (iii) supermarket game theory and (iv) resource allocation in Multiuser Multi-Carrier CRNs (MMC-CRNs) using game and supermarket game theory. Furthermore, we have tried our best to provide simple definitions and scenarios to facilitate a better understating of the problem of game/market resource allocation in MMC-CRNs.

1.1 Motivations for using game/supermarket game theory in MMC-CRNs

Game and supermarket game theory have become important fields of study for resource allocation in CRNs. This is because both "game theory' and "supermarket game theory' have proven to be a powerful decision making structure that able to provide excellent performance for CR nodes compared to that in ordinary optimization theory [4]. Moreover, game/supermarket game theory provides fast convergence of resource allocation algorithms to a common point (i.e., steady-state point), which is another important issue to consider when adopting game/supermarket game theory in CRNs. The motivations behind adopting game and supermarket game theory in MMC-CRNs can be summarized as follows:

(1) Interaction among independent users: In CRNs, there are two types of users (i.e., PUs and CRs), also called decision makers, with conflicts of interest, interacting with each other independently, trying to access the same spectrum band. This interaction adds certain obstacles in analyzing the problem of resource allocation in MMC-CRNs. Game theory, in contrast, appears to be one of the most attractive tools for removing these obstacles because it is mainly used to model scenarios where the action of one player impacts/conflicts with that of other players in the network [4]. Moreover, the availability of a common solution in game theory such as the Nash equilibrium and Nash bargaining add another advantage in modeling the problem of resource allocation via game theory.

(2) Spectrum supermarket and real supermarket: The behavior of PUs and CRs in allocating their resources in MMC-CRNs is quite similar to the interactions among people in actual markets. Both include the following features: (i) Pricing, where the owner of the spectrum can gain benefits by renting the available spectrum holes to the tenants in the network (i.e., CR nodes). Thus, mutual benefits exist whereby the PUs improves their revenue and CRs enjoy access to the band for their needs. (ii) Auction, where CRs compete with each other in an auction scenario to obtain access to certain bands. The similarities between the concept of CRs and the interaction among people in a real supermarket make the adoption of economics concepts in analyzing the problem of resource allocation in MMC-CRNs another attractive tool.

1.2 Research Contributions

In this article, we have provided a tutorial on the application of game and supermarket game theory to the problem of resource allocation in MMC-CRNs. This tutorial is driven by the following problems: (i) how to build a cognitive radio network on a licensed spectrum; (ii) how CRs allocate their resources without harming the owner of the spectrum; (iii) how to apply game/market theory to the problem of resource allocation in MMC-CRNs; (iv) how to define the solution associated with game/market theory (e.g., Nash equilibrium, Nash bargaining), and (v) how to prove the existence and uniqueness in the defined game/market. We address these issues by making the following contributions:

1) Spectrum sharing and spectrum access in CRNs: We have provided a simple introduction

to the concept of spectrum access and spectrum sharing techniques in CRNs. This includes related issues, objectives, and comparisons for recently developed spectrum sharing/access technique in CRNs.

2) Game theory and supermarket game theory: This includes the following:

* We have provided a simple introduction and analysis to the fundamentals of (i) non-cooperative game theory, (ii) cooperative game theory, and (iii) market theory.

* Instead of mathematical approach for the NE, we have proposed a visual mathematical approach that facilitates a better understanding of the mathematical solution of the game (i.e., Nash equilibrium).

* We have proposed several definitions, scenarios and examples for the application of game and market theory to the problem of resource allocation in MMC-CRNs.

3) Resource allocation and management in MMC-CRNs: We have included a survey of recent and related studies in the literature on the resource allocation problem in MMCCRNs based on game/supermarket game theory by summarizing its main features and objectives.

To the best of our knowledge, this paper is the first tutorial that offers concrete descriptions related to the resource allocation problem in MMC-CRNs based on game and supermarket game theory.

1.3 Organization of the paper

This tutorial is organized as follows. In Section 2, we introduce the concept of (i) CR architecture, (ii) resource management in CRNs, and (iii) MMC-CRNs. The concepts of game theory and its solutions are presented in Section 3. Spectrum trading and supermarket game theory are explored in Section 4. An overview of resource allocation in MMC-CRNs and a survey of the related studies in the literature are presented in Section 5. Open research directions and the conclusion of the study are presented in Section 6 and Section 7, respectively.

2 Cognitive Radio Network

This section summarizes the main concept for (i) CRN models, (ii) spectrum sharing and spectrum access techniques in CRNs, and (iii) multicarrier techniques for CRNs.

2.1 CRN Models

In CRNs, there are two general types of models that can be defined as follows [5], [6]: (i) Infrastructure-based model: A CR base station, abbreviated as "CRBS", is the main component in this approach and facilitates the residence of CRs in the licensed spectrum. Moreover, monitoring the spectrum band utilization and guiding the CRs to the vacant band is another feature of CRBS. (ii) Ad-hoc-based model: No permanent infrastructure exists in this approach. Thus, CRs must communicate among themselves independently to determine their actions while minimizing the amount of interference generated to PUs based on their own monitoring [6]. Table 1 provides the main components for both approaches. In this tutorial, the application of game and supermarket game theory is considered in both infrastructure and ad-hoc approaches.

2.2 Spectrum Sharing and Recourse Management in CRNs

In this section, we summarize the features and concepts of spectrum sharing and spectrum access in CRNs.

2.2.1 Spectrum Sharing in CRNs

A key challenge in CRN spectrum sharing is to answer the following question: "how do you allocate transmission resources (e.g., power and subcarrier) efficiently among CRs over a wide range of available spectra with the available activities of neighboring PUs?" [5] To be specific, spectrum sharing in CRNs must take into account the following essential issues: (i) providing the capability to maintain good QoS for CRs and (ii) minimizing the generated interference to the PUs by wisely assigning the transmission resources to CRs. To address the above mentioned issues, two main spectrum sharing techniques in CRNs are briefly described as follows [7]:

1) "Open spectrum sharing': If CR users only access the unlicensed band, e.g., scientific and medical band (ISM band) or TV white space, then the spectrum sharing model is defined as an "open spectrum sharing', where all CR users have the same rights among themselves to utilize the spectrum and allocate their resources accordingly. Fig. 1 provides an example of open spectrum sharing.

2) "Hierarchical spectrum sharingIf CR users access the licensed spectrum together with PUs, then the spectrum sharing model is defined as a "hierarchical spectrum sharing where the CRs strictly follow certain policies (e.g., spectrum sensing) to access the available spectrum. Fig. 2 provides an example of hierarchical spectrum sharing.

Moreover, hierarchical spectrum sharing can be divided into two main approaches: (i) overlay spectrum sharing and (ii) underlay spectrum sharing. The main features of the overlay and underlay approaches are summarized based on the following:

1) Overlay spectrum access: CRs, in this approach, have permission to access the available spectrum opportunistically/rationally if and only if the spectrum is not being occupied by the PUs. Moreover, CRs are able to use a portion of their power for cognitive transmission and the rest of the power to help (relay) the transmission of PUs [8]. The main objective of this technique is to manage and control the access of CRs to spectrum holes [5], [9]. Fig. 3 shows an example of overlay spectrum access. 2

2) Underlay spectrum access: CRs, in this approach, share the spectrum simultaneously with PUs. Thus, PUs must be protected by applying a spectral mask on the CRs signals to make the generated interference from active CRs below the acceptable threshold for PUs to run smoothly and to provide fair communication services among PUs and CRs [8]. Fig. 4 illustrates an example of underlay spectrum access.

Both spectrum access techniques have been widely adopted in the literature to allow CRs to communicate among them using the licensed spectrum band. However, more attention is being given to analyzing the underlay spectrum access caused by the difficulties associated with controlling the behavior of CRs attempting to minimize the generated interference to the owner of the spectrum.

2.3 Multiuser Multicarrier CRNs (MMC-CRNs): Concepts and Interference Analysis

In CRNs, the key features of CRs are (i) their ability to sense the available spectrum band and (ii) their ability to communicate with each other without interfering with the service of PUs to obtain better spectrum utilization than that in the fixed spectrum approach [10]. To fulfill the first point1 2, CRs must be prepared with spectrum sensing capability, and to achieve the second point, the PHY of the CR must be sufficiently flexible.

The multicarrier technique, in contrast, is envisioned as a promising candidate for CRNs that can satisfy the PHY issues for CRs. Moreover, multicarrier technique, abbreviated as (MC) have been seen to provide reliability and flexibility in allocating the available resources among CRs, which results in a better communication environment among CRs and PUs [1113]. Additionally, MC-based CRNs can provide excellent coexistence among PUs and CRs based on the following abilities: (i) nulling the subcarriers that are currently occupied by active PUs and (ii) nulling the subcarriers that may produce certain amounts of interference for other users in the network [14].

Orthogonal frequency division multiplexing (OFDM) is a special case of MC techniques and is considered one of the most promising multicarrier candidates that can provide proper performance and flexibility in dynamically allocating spectrum holes among CRs. Moreover, adopting OFDM to the problem of resource allocation in CRNs facilitates the monitoring of the PU's activity and the occupancy of spectrum holes accordingly [3]. Another multi-carrier candidate that can be adopted in the problem of resource allocation is the filter bank multicarrier (FBMC2) technique [15]. Compared to OFDM, (i) FBMC can provide better spectral efficiency in CRNs by separating the transmission of PUs and CRs through filtering [16], and (ii) FBMC promises very low out-of-band energy for each subcarrier signal [17]. Knowing this, in multiuser multicarrier networks, a multiple access scheme is required, e.g., an orthogonal frequency multiple access technique (OFDMA), to allocate both subcarriers and power to CR nodes.

To demonstrate the idea of MMC-CRN and the related issues, we provide the following motivating example

Motivating Example_1: "MMC-CRN Architecture and Interference Analysis": Assuming that we have a CR-based-OFDM network, consisting of two types of mobile radio devices (PUs and CRs) coexisting in the same geographical area and communicating using the same band as shown in Fig. 5-a, where communication links and channel gains of different links can be defined as follows: (i) the sold lines indicate the intended signal links; (ii) the spotted lines are the interference links; (iii) [g.sup.c.sub.f] and [g.sup.p.sub.k] are the interference gains from CR-to-PU and PU-to-CR, respectively; and (iv) the superscripts (c) and (p) refer to the cognitive radio and the primary users, respectively.

Moreover, in MMC-based CRNs (i.e., OFDM), both CRs and PUs exist in side-by-side spectrum bands [18] as shown in Fig. 5-b. Thus, a mutual interference among PUs and CRs arises in this scenario and requires special consideration to maintain acceptable performance in both networks [19]. Assuming that CRNs consist of K CRs and the available band is divided into N subcarrier with [DELTA]f bandwidth, based on Fig. 5-(a & b), the generated interference from CRs to the band of active PUs can be defined based on the following definition:

Definition 1: [19-21]: Interference generated by the k-th CR access on
the n-th subcarrier to the l-th PU denoted by [I.sup.PU.sub.n,l] can be
defined as the integration of the power density spectrum of the n-th
subcarrier ([[phi].sub.n]) across the l-th PU band (Band-Z).
Mathematically speaking, the interference introduced by the CR's signal
can be modeled as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [d.sub.t] is the distance between the n-th subcarrier and the
l-th PU's spectrum band, [p.sup.k.sub.n] is the transmitted power for
the active CR, gC is the channel gain of the interference link
from CR-to-PU and [B.sub.l] is the l-th PU' bandwidth.


Note that the active PUs also generates an amount of interference to the CRs, and that amount of interference should be formulated mathematically3 to provide for a concrete analysis for mutual interference in MMC-CRNs.

3. Application of Game Theory in MMC-CRNs

Details related to the concepts and applications of game theory including both "noncooperative game theory" and "cooperative game theory" are discussed in the following sections.

3.1 Game theory: Basic Concepts

Game theory was first introduced by J.V. Neumann and O. Morgenstern in 1944 [22] and is extensively used in microeconomics. Its application has commonly been recognized as a great tool for analyzing several engineering problems. Game theory can be defined based on definition 2.

Definition 2: " Game theory" [23-25]: Game theory is a branch of
applied mathematics that can be adopted to study situations where
the actions of several decision makers (also called players) are
in conflict. Mathematically speaking, a game can be defined as
[22], [25] [G.sub.ame] = < K, A, [[pi].sub.i] > , (2)

where

1) K is a finite set of decision makers (players);

2) A is the Cartesian product of the sets of actions available to
each player; and

3) [[pi].sub.i] is the utility/payoff/objective functions of player i,
which is a function of the action chosen by player i
([a.sup.ction.sub.i]) and the actions chosen by all of the players in
the game but not that of player i ([a.sup.ction.sub.-i]).


Moreover, game theory can be classified into two main approaches: (i) Non-cooperative game theory: In this approach, the decision makers (or players) behave selfishly, aiming to maximize their own revenue. (ii) Cooperative game theory: In this approach, the players behave cooperatively to maximize the revenue of their network.

Furthermore, the strategies in game theory can be divided into two types: (i) pure strategy and (ii) mixed strategy. Table 2 gives a brief comparison among players' strategies in game theory.

In addition, it is worth mentioning that in [26] and [27], the authors provide a comprehensive survey on the application of game theory in CRNs and general wireless networks respectively. Furthermore, details related to fundamentals and concepts of game theory have been included as well. Hence, readers are advised to refer to [26] and [27] for more details regarding the mathematical formulations that illustrate the concepts of game theory. Our work, in contrast focuses on the applications of game theory and supermarket game theory to the problem of resource allocation in MMC-CRNs.

To simplify the concept of game theory and to show how the components of game theory and the elements of MMC-CRNs related to each others, we provide the following scenario as follows

Motivating Scenario_1: assuming that we have an OFDM-based CRNs coexisting with primary user provider in the same geographical area (i.e., similar to the deployment illustrated in Fig.5.a and 5.b). The CRNs consisting from three users competing with each other in order to allocate the subcarriers left over by the primary user. Game theory, in contrast, shows to be one of the most attractive tools to analyze this scenario because of the availability of group of users competing with each other to win a band for their transmission purposes. Hence, the component of game theory can be translated to the entities of MMC-CRNs according to Table. 3

In the following sections, details of both branches of game theory are presented by providing definitions, examples, scenarios and discussion regarding the common solution when a game is adopted. Hence, the interested readers can better understand the concept of game theory and its applications in the problem of resource allocation in MMC-CRNs.

3.2 Non-cooperative Game Theory Approach: Concepts and Theorems

Non-cooperative game theory is widely adopted in modeling resource allocation problem in CRNs and can be defined based on definition 3:

Definition 3: [23], [24]: Non-cooperative game theory, abbreviated as
NCGT, is an approach that can be adopted to resolve the conflicts in a
given scenario where the players are selfish and make their decisions
independently.


The motivation of adopting NCGT in the problem of resource allocation in MMC-CRNs is the noticeable improvement in term of efficiency, spectrum utilization and the ability to guide selfish players to more stable resource allocation outcomes. To familiarize the reader with the concept of NCGT, we provide the following scenario:

Scenario 2 "Application of NCGT in MMC-CRNs": NCGT is considered to be
one of the most powerful tools used to investigate the problem of
resource allocation in MMC-CRNs. In this scenario, the rational players,
also called CRs, compete with each other to access vacant subcarriers.
Thus, NCGT is the preferred approach to explore this scenario because
it is generally applied to study situations in which the players'
objectives are in conflict. The game in this scenario can be modeled
as follows:

1) Players K = {1, 2, ...,K}: Players in the MC-CRN are CR nodes.

2) Players' strategy A = [A.sub.1] x [A.sub.2] x ... x [A.sub.N]: The
set of strategies available to tenants. This includes subcarriers, bit
loading and power allocation based on the local information available
to players [28].

3) Utility function [[pi].sub.i] : A [right arrow] R is the objective
function that each player wishes to maximize (e.g., the player's rate
maximization) [29].


3.2.1 Common Solution to NCGT

When using NCGT, one should answer the following question: "What will occur when interactions among rational players take place in certain applications?" One of the most commonly used solutions to predict the output of a game is the Nash equilibrium, which can be defined based on definition 4.

Definition 4: [23, 24], [30]: The Nash equilibrium (termed NE) of a
NCGT is an action profile such that no player can gain any benefit by
varying his own strategy unilaterally.


To simplify the idea of the NE, we provide a visual approach to describe how the NE works in a given scenario as presented in Fig. 6.

Another significant issue in the solution of NCGT (or NE) is the investigation of two important properties: (i) Existence of an NE: The existence of an NE can be obtained using specific mathematical properties related to certain utility functions (e.g., supermodularity and supermodular games) [31]. (ii) Uniqueness: In addition to the existence property, the uniqueness of an NE must also be considered in the solution to NCGT. Moreover, Theorem 1 and Theorem 2 provide the necessary conditions for both properties as follows:

Theorem 1 [29], [32]: An NE exists in a game [G.sub.ame] = <K, A, {[[pi].sub.i]> if for [for all]i [member of] K, the following conditions hold:

1) The action profile of player i is a nonempty, convex and compact subset of some Euclidean space.

2) The utility function [[pi].sub.i] is a continuous and quasi-concave function over its action set. Theorem 2: An NE in NCGT is unique if a game [G.sub.ame] = (K, A,{[[pi].sub.i]} modeled using the

following special game technique is thus shown to reach a unique NE:

1) Potential game [33] (5);

2) Standard function [34] (6).

If a utility function in NCGT is carefully selected and the above mentioned theorems are fulfilled, then the NE is guaranteed to exist.

3.3 Cooperative Game Theory Approach: Concepts and Theorems

In contrast to NCGT, players in cooperative game theory (abbreviated as CGT) are collaborating with each other wisely to maximize the total utility of their network, and, thus, the performance of the network can be improved accordingly. In this section, we discuss two popular forms of cooperative game theory: (i) bargaining game and (ii) coalition game.

3.3.1 Bargaining Game

In bargaining game, abbreviated as BG, the players have a choice to cooperate and negotiate with each other. Thus, the players have the opportunity to reach a commonly beneficial agreement where all the players gain the maximum profit [35], [36]. The idea of a bargain game can be explained via the following scenario:

Scenario 3 "Application of CGT (BG) in MMC-CRNs": BG is a powerful tool
that provides fairness among players in the problem of resource
allocation in MMC-CRNs. Players (i.e., CRs) cooperate with each other
without any competition to maximize the revenue of their network. To
simplify this scenario, we consider a two-player BG that negotiates to
allocate subcarrier in OFDMA-CRN. Thus, the BG in this scenario can be
described as follows:

1) Conflicts and fairness issue: Free sub-carriers are available to
both players. However, some sub-carrier is good for both users, and
if player 1 gains a greater amount of resources, player 2 will gain
a lesser amount. Thus, to maximize the network's total revenue,
both players search for a fair distribution of the available
resources (e.g., to obtain the minimal rate) via negotiation [35].

2) Players issue: K = {1, 2} two CR players in MMC-CRN.

3) Agreement issue: Player 1 and player 2 receive their own
utilities for their collaboration. Assume [[pi].sup.1] and
[[pi].sup.2] are the utility functions for player 1 and player 2,
respectively. In contrast, let [[pi].sup.1.sub.min] and
[[pi].sup.2.sub.min] be the minimum utilities that both players are
happy to receive; otherwise, they will not negotiate [37].

4) Modeling issue: 2-player BG is modeled by the pair of utilities
for the two players and the minimum utilities that players received
at the initial agreement. Let S be a compact and convex subset of
^K that represents the set of all possible utilities that players
can obtain if cooperating via negotiation. Let [[pi].sub.min] =
([[pi].sup.1.sub.min], [[pi].sup.2.sub.min]) be the initial
agreement point. The pair (S, [[pi].sub.min])is called the 2-player
bargaining problem [38], [39]. Moreover, the objective in this
scenario is to maximize [[pi].sup.1] and [[pi].sup.2] concurrently.


Similar to NCGT, there is a common solution used for CGT, which is the topic of the following subsection.

3.3.2 Common Solution to CGT

One of the most commonly used solutions in CGT is called the Nash bargaining solution (NBS). This solution provides an optimal and fair resource allocation among players and can be defined as a function [bar.[pi]] = f (S, [[pi].sub.min]) that assigns a BG problem to a unique element of S based on the Nash axiom constraints7 [36].

Moreover, the two important properties (i) existence and (ii) uniqueness are also associated with NBS and must also be examined in the problem.

Theorem 3 "Existence and Uniqueness of NBS": A unique and fair NBS f (S, [[pi].sub.min])can be obtained by maximizing a Nash product term based on

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)

Proof: If the problem of resource allocation in MMC-CRNs is formulated as in (3), then the NBS satisfies all the Nash axioms and is shown to provide a fair and unique solution as presented in [37], [40].

3.3.3 Coalition Game

The second type of CGT is called a coalitional game and is abbreviated as CG. CGs have been shown to be an important tool for designing efficient, fair, and collaborative strategies in CRNs and can be divided into three categories (8) [41]: (i) canonical coalitional games, (ii) coalition formation games, and (iii) coalitional graph games.

CG theory describes how a set of players collaborate with each other by creating collaborating groups and can be defined as follows:

Definition 5: [36, 37], [41]: Let the set of players be denoted by
K and a nonempty subset (coalition) by S (i.e., S [subset] K). For a
K-player game, any nonempty subset of players (i.e., S) is then called
a coalition.


To demonstrate the idea of a K-player CG, we provide the following basic example:

Motivating Example 2: "Modeling of a Coalition Game in MMC-CRNs": Consider the problem of subcarrier allocation in MMC-CRNs. The concept of a CG can be adopted to model K-players based on the following steps [37]: (i) Forming step: K players are grouped into pairs, named a coalition. (ii) Two-player negotiation step: Each coalition follows the procedures listed in (scenario 2) so that pairs in each coalition can negotiate with each other and exchange the information about available subcarriers. (iii) Reforming and convergence step: All the players are regrouped and continue their negotiation until convergence occurs.

4 Application of Supermarket Game in MMC-CRNs

In this section, we introduce the concepts of supermarket game theory, which includes the following: "pricing theory", "auction theory"', and "oligopolistic competition" and their relevance to game theory.

4.1 Supermarket Game Theory: An Introduction

The concepts of a game as labeled in section (3) highlighted the following fact: game theory provides mathematical tools to study the scenario where rational players interact with each other. Based on this fact, game theory can be applied to a real supermarket scenario to study how individuals interact and negotiate with each other as buyers and sellers in the arena of a supermarket. The application of game theory to the market scenario is extremely interesting in the field of MMC-CNR for the following main reasons: (i) PUs enter the supermarket with the unused band as a commodity for sale to increase their revenue; and (ii) CRs, in contrast, enter the market looking for a commodity to buy (i.e., spectrum holes) to conduct a transmission with their partner. Thus, game theory can be applied to a spectrum supermarket to study the interaction among buyers and sellers accordingly.

4.2 Pricing Theory

Pricing theory was first introduced and adopted in the arena of economics. In the field of spectrum market approaches, pricing theory becomes one of the important tools in the problem of resource allocation for the following reasons: (i) In the case of NCGT, pricing can provide an efficient NE by guiding selfish players to a more efficient operating point9 [29]. (ii) In the case of CG, pricing can provide a better negotiation environment and fair distribution of the available resources so that the seller/buyers of the spectrum (i.e., PUs/CRs) are satisfied. (iii) Finally, pricing acts as a punishment technique for those buyers that generate certain amounts of interference to PUs, and, subsequently, interference to the owner of the spectrum can be minimized. To understand the general idea behind pricing, we have provided the following definition:

Definition 6: During spectrum trading in the distributed spectrum
market, the pricing function can be defined as the cost that CRs
must pay to PUs in terms of the performance degradation that may
take place in the primary networks (PNs). However, in a certain
scenario (e.g., centralized, downlink/uplink), CRs must buy
spectrum for their transmission purposes, and, subsequently, prices
are given to the PUBS as a cost of using the spectrum.


4.3 Auction Theory

Auction theory [42] is extensively used in the field of economics to determine, for example, the value of commodities that have uncertain prices. Recently, it has been applied to solve issues related to the problem of resource allocation in wireless networks. The common auction scenario can have the following components [43, 44]: (i) bidders, (2) a seller, (3) an auctioneer, and (iv) the commodity. Table 3 provides a mapping between basic components of auction theory and the entities of MC-CRNs.

Generally speaking, the auction supermarket adopts the following scenario: (i) The buyers compete with each other by submitting an (ask) asking about the price of the product to be sold in the spectrum market to obtain one of the available commodities. (ii) The sellers, in certain scenarios, compete with each other to obtain additional buyers to increase their revenue by submitting a (bid) indicating the bidding price for the requested product [43]. Hence, game theory is the best mathematical tool to analyze the behavior of sellers, buyers and auctioneer in an auction scenario. Accordingly, the application of an auction as a game has generally been adopted in the problem of resource allocation in CRNs. In the following paragraph, we provide a scenario of the application of an auction game in MMC-CRNs as shown below.

Scenario 4 "Application of Auction Game in MMC-CRNs": An auction
game can be adopted in MMC-CRNs to encourage both sellers and
buyers in the network to select their strategies wisely to achieve
the network's objectives [43]. The main functions of auction game
scenario are as follows:

1) Players K = {1, 2, ...,K}: Players in the auction game are both
sellers (PUBs) and buyers (CRs).

2) Players' strategies: The action set of each player is a set of
asks submitted by rational buyers asking for available subcarriers
and a set of bids submitted by rational sellers informing buyers
about the cost for the available subcarriers.

3) Game objective (payoff): The objective of the auction game is to
reach an equilibrium strategy among buyers and sellers, where
buyers are satisfied with the cost and the sellers are satisfied
with the profit.

Auction solution: The NE and its details (i.e., existence and
uniqueness) are considered to be a common solution in auction
games.

...Continue to next page for Scenario

3


In Fig. 7, the buyers are the CR nodes, the seller is the primary user base stations (PUBS) and the auctioneer is the PUBS itself. The sellers offer the unused subcarrier to the buyers at a certain price to increase their revenue. The buyers can accept the offer and make their transmissions accordingly.

4.4 Oligopoly Market Competition

When a small number of firms compete with each other to maximize their revenue by managing the quantity or the price of the offered commodity, then the market can be called an "oligopolistic market" [45] with the following assumptions [46]: (i) few firms are available in the market; (ii) the firms compete with each other independently to increase their revenue; and (iii) each firm should take into account the available strategies of other firms in the market.

Moreover, the behavior of firms in an oligopoly market (i.e., interaction and competition) can be modeled using the concept of game theory. However, modeling an oligopoly market as a game requires different models that have different supermarket structure and different strategies [47]. Table 5 summarizes features of the most familiar oligopoly game in the literature. To facilitate a better understanding to the concept of oligopoly market game, we have provided the following example:

Motivating Example_3 [50]:"Modeling of Oligopoly-Bertrand Game in MMC-CRNs"

Assuming that Z-PU spectrum service providers compete with each other in an MMC-CRN oligopoly-Bertrand scenario, the resource allocation problem can be described based on the following: (i) commodities are the vacant subcarriers offered by PU spectrum providers, (ii) firms (i.e., players) are the spectrum providers that compete with each other to obtain additional buyers (i.e., CRs) to maximize their profit, (iii) consumers are the CRs that willing buy/rent good commodities (i.e., subcarriers with less interference to PU) at a reasonable price, (iv) strategies of the firms are related to the supplied quantity or offering price, (v) the payoff of a firm is linked by its surplus function (revenue minus cost) for renting vacant subcarriers to CRs and (vi) the game solution is the NE.

Motivating Example_4: "Modelling of stacklberg in uplink MMC-CRNs"

Assuming an uplink scenario in OFDMA based CRNs as shown in Fig.8

The PUBS is the owner of the spectrum and their users (i.e., PUs) transmit to the PUBS for free of charge. CRs, in contrast, need to pay to the PUBS in order to get subcarrier for their needs. The strategy between the PUBS and CRS can be modelled according to Stacklberg market game with the following assumptions: (i) PUBS is the leader of market game, (ii) PUBS sell its vacant band and charge a price for each CR to maximize its profit, (iii) the CRs are the followers in this scenario and need to follow the pricing policies generated by the PUBS, and (iv) after all prices distributed by PUBS, the CRs make a decision to utilize the subcarrier with controlled power to maximize their utility function based on NCGT.

Note that the same example can be simply applied to Cournot and Bertrand model by following the features listed in Table 5.

5 Resource Allocation in MMC-CRNs

5.1 Resource Allocation in MMC-CRNs: An Overview

The resource allocation problem (e.g., power and subcarrier allocation) in MMC-CRNs brings to academics certain challenges because of the following facts: (i) two different mobile radio users (i.e., PUs and CRs) interact with each other, transmitting independently within the same band, and may be based on different standards [16], (ii) CRs are rational, aiming to allocate their resource independently and, in some scenarios, selfishly and (iii) the interference that arises from CRs-to-PUs and vice versa is another concern that must be treated carefully in MMC-CRNs.

The first two points make game theory a promising tool for resource allocation in CRNs because game theory is extensively applied to study situations with conflicting interests. Moreover, in multicarrier techniques (e.g., OFDM and FBMC), the PUs leave some unused subcarrier during their idle period. Thus, CRs have the opportunity to utilize unused subcarriers. In another words, the CR pays the owner of the spectrum to temporarily rent his vacant bands. Therefore, a mutual benefit exists in this scenario, where the rental users (i.e., CRs) take the advantages by utilizing the vacant spectrum for their transmission purposes, and the owner of the spectrum can maximize their revenue accordingly [3]. This basic concept makes adopting market theory in the problem of resource allocation another promising solution. In addition, an overview of the problem of resource allocation in MMCCRNs is shown in Fig. 8 and can be described based on the following example.

Motivating Example_5: "Resource allocation problem in OFDMA-CRNs": Assuming that K-CR players are available in the network with N OFDM subcarrier frequency distributions as shown in Fig. 8. Thus, the problem is to structure the following: (i) Problem formulation, which includes the design of the utility function (e.g., rate maximization) with a set of constraints (e.g., channel/power/interference constraints). (ii) Subcarrier allocations, abbreviated as SA, (i.e., subcarriers to CRs allocation matrix SA = [[[sa.sub.k,n]].sub.KxN]) where each subcarrier is assigned to only one CR. (iii) Non-cooperative power allocation game, abbreviated as NCPA, for each subcarrier (i.e., PA = [[[p.sub.n]].sub.Nx1]), which can be determined based on maximum power and interference constraints.

The optimal solution to the resource allocation problem in MMC-CRNs is, in general, an NP hard problem. Thus, the suboptimal scheme is preferred in such a scenario and can be achieved by decomposing the resource allocation problem into two sub-problems (i.e., an SA problem and a NCPA problem). Moreover, the optimal NCPA algorithm can be achieved via a Lagrangian technique.

Furthermore, the problem of resource allocation in MMC-CRs can take the following three forms: (i) uplink resource allocation with multiple local power constraints (e.g., see [12], [52]-[53]); (ii) downlink resource allocation with global power constraints (e.g., see [54][55]); and (iii) distributed resource allocation as in an ad-hoc scenario (e.g., see [56]-[57]).

5.2 Resource allocation in MMC-CRNs via game/supermarket game theory

Studies on resource-allocation-based game theory in multicarrier wireless networks can be divided into two general approaches [58]: (i) rate-adaptive games as in [59] and (ii) margin-adaptive (i.e., MA) games as in [60]. However, another approach can be used when using game theory and supermarket game theory: (iii) spectrum-market game, which can be either rate-adaptive, margin-adaptive or a pure spectrum market as in [45], where CRs are required to follow certain rules to obtain acceptable commodities (i.e., frequency spectrum), while the owners of the market increase their revenue accordingly.

In the case of rate-based resource allocation, the problem is normally formulated to maximize the total rate of the network subject to subcarrier, power and interference constraints as shown in Fig. 9, whereas in margin-based resource allocation, the problem is formulated to minimize the total power subject to subcarrier and quality of service requirement for each user in the network.

For the scenario of MMC-CRNs, most of the studies conducted in the literature focused on rate-adaptive compared to margin-adaptive classes because the latter technique makes the optimization problem more complex compared to the rate adaptation technique. Furthermore, the spectrum market game in the problem of resource allocation in MC-CRNs has received light attention, and more effort is needed in the field of spectrum market game theory.

5.3 Discussions on related works

In this tutorial, we have classified the studies conducted in the literature into five classes as shown in Table 6.

Note 1: According to Table 6 class (B), the problem of resource
allocation in multicarrier non-CR scenarios is presented (i) to
allow the readers to become familiar with the concept of resource
allocation in multicarrier methods using both game and supermarket
game theory and (ii) to show that moving from the non-cognitive
scenario to the cognitive model can be easily performed by taking
into account the interferences generated from CRs-toPUs (i.e., eq.
1) and the interference generated form PUs-to-CRs (i.e., eq. 4 in
Appendix I) accordingly.


In addition, to add to the presentation for the mentioned classes, we have provided scenario 5 to further assist readers. Moreover, all the related studies in the literature were classified similar to the details listed in Scenario 5.

Scenario 5: Applications' classes: We
assume that we have been asked to
analyze the problem of resource
allocation in multicarrier wireless
network based on the following
assumptions:

Research Type          Problem           Problem Approach

Tutorial        Resource allocation in   General approach
                       MMC-CRNs             (Tutorial)

Based on Table 5, the above mentioned
assumptions can be translated to the
following codes:

Research Type      Problem to solve      Problem Approach

A.2                      B.1                    C.3

Research Type   Cell Model    Network Model

Tutorial        Single cell    Distributed

Based on Table 5, the above mentioned
assumptions can be translated to the
following codes:

Research Type   Cell Model    Network Model

A.2                 D.1            E.2


Following the listed classes in Table 6, we have provided a summary of studies related to the resource allocation problem in multicarrier technology based on game and supermarket game model as shown in Table 7.

In the following sub-sections, we demonstrate the main features of related studies conducted in the literature.

5.3.1 Game and supermarket game in non-cognitive MC scenarios

Game and supermarket game theory have been recently adopted to address the problem of resource allocation in wireless networks (see, for example, [59], [63], [64], [66], [70] and [71]). Table 8 summarizes the main features of a number of selected studies conducted on the resource allocation problem in multicarrierwireless networks using both game theory and supermarket game theory.

In the case of MMC-CRNs, game theory and supermarket game were proven to provide efficient and effective spectrum sharing among CRs and the owner of the spectrum because they can properly define the interaction and competition among players [47]. There are a number of studies that adopted game and supermarket game theory in multicarrier CRNs to address the related issues to spectrum access (i.e., power, subcarriers and rate) as in [43], [61], [64], [67-69], [72-76]. To be more specific we provide a review to a number of related studies conducted in the literature as shown below.

In [61], a spectrum monopoly-market scenario based on non-cooperative game theory was proposed for OFDM-based CRNs. The most interesting point in this work is that the CRs performing two interesting tasks as follows: (i) using part of the leased band to help the PUs by relaying tier data from the source to destination and (ii) use the remaining part of the leased band for their own activities. Moreover, the PUs enters the market aiming to sell certain amount of its vacant band to CRs and the CRs, in contrast, enters the market aiming to transmit with optimal power in order to fulfil the above mentioned tasks. The authors adopted non-cooperative game in order to find optimal power for the CRs in the leasing-market scenario.

Instead of Stackelberg game, the authors employed auction to solve the spectrum leasing scenario where the CRs are involved in the leasing decisions which consider another interesting contribution of this work among others in the literature. The authors guided the readers to some selected references for the mathematical verification of the existence and uniqueness of the NE. However, the convergence of the proposed algorithm to a stable point is a bit slow. Hence it is not appropriate for more particle scenario.

More complicated RA scenario in MMC-CRNs based on non-cooperative game has been proposed in [64]. Instead of multiuser-single cell scenario, the authors proposed RA algorithm in multiuser multi-cell MC-CRNs which resulted in NP-hard problem. To tackle this problem, the authors adopted the multiple access channels (MAC) technique in order to convert their problem to a concave optimization problem which is one of the novel contributions of this work. Non-cooperative game theory based on MAC technique has been adopted in this work to allocate the subcarrier and power in uplink scenario. Existence and uniqueness of the NE are validated mathematically. However, the authors didn't provide any evidence to show that the proposed power algorithm convergence to unique NE via simulation. Moreover, the cheating scenario among the selfish CRs has been ignored in this work.

One of the most important problems to tackle while allocating subcarriers among CRs in MC technique is how to mitigate the generated interference to the owner of the spectrum (i.e., PUs). This significant problem has been considered in [67] in order to designed not only efficient RA algorithm but also optimal subcarrier allocation with minimal interference in MC-CRNs. Firstly, the authors adopted an interference mitigation objective in the utility function and defined the potential function where the NE is always guaranteed. Secondly, the authors proposed modified subcarrier-game scheme know as autonomous number of subcarrier selection (ANSS) method which considered as etiquette provider for the whole network. Through ANSS scheme the players are allowed to have some interaction among them before the start of the real game. This makes each player aware of its environment and the available recourses and can easily measure the amount of interference from neighbor players within its radius of interference. The novelty of this work comes from introducing potential game with means of cooperation and self-awareness in the player' utility function and introducing sequential best response play in order to make the ANSS-game model converge to unique stable point (i.e., NE). However, the proposed algorithm shows slow convergence to a stable point which is the main drawback for the proposed algorithm.

An overlay spectrum sharing based on game-pricing approach in MC-CRNs has been considered in [72]. The main contribution of this work is by adopting pay-off function that comes with two parts: (i) rate-based utility function and (ii) pricing function. The pricing function, in contrast, composed of two parts in order to manage: (i) the interference generated among CRs in the network represented by normal pricing function, and (ii) the negative effect from active CRs to PU' sub-band represented by exponential pricing function. Accordingly, sufficient and fair spectrum sharing can be achieved in this work by provide adequate protection to the PUs. Furthermore, the existence and uniqueness of the proposed objective function has been verified mathematically and via simulation as well. The authors considered a distributed scenario; however the cheating scenario among the selfish CRs has been ignored in this work. Unlike [61] and [67] the proposed algorithm in [72] resulted in a fast convergence to the NE. Hence, it is more appropriate for more practical scenario.

Resource allocation in MC-CRNs based on market-game has been considered in [73]. The most interesting issue in this work, among others, is that the authors adopted Colonel Blotto market game to model the problem of subcarrier and power allocation in both uplink and downlink scenario. Unlike [64], the authors proposed a simple optimization problem by adopting interference temperature constraint instead of global power constraint and Blotto game used to allocate the resources among the players which resulted in a fair allocation and fast convergence to NE. Moreover, the cheating scenario has been introduced in this work which is another obvious issue in this work compared to that in [72]. The existence and uniqueness of the NE have been verified mathematically and via simulation as well. However, the convergence of the proposed algorithm is slightly slower than that in [72].

In [74], the authors proposed new and dynamic pricing scheme in a competitive spectrum-supermarket. The noticeable advantages of this work compared to other studies related to spectrum market, is that the buyers play an important role in the convergence of the market by evaluating the spectrum sellers in a different way based on the quality of goods provided by sellers and the prices offered by the sellers. The sellers, based on buyer's evaluation, are trying their best to show the available spectrum at affordable prices to attract not only quality sensitive buyers but also the price wise buyers. Therefore, the performance of the spectrum market can be improved accordingly. Game theory has been adopted in [74] to analyze the profit of the sellers. Convergence of the market has been well investigated by simulation and the market convergence to stable points where all buyers and sellers are satisfied in their commodities and profit respectively. However, the proposed market mode is not practical in heterogeneous spectrum market where many buyers and sellers are available because of the long time required by the buyers to evaluate different goods with different prices provided by different sellers.

The authors in [76] proposed an energy-efficient algorithm for joint power and subcarrier allocation in the uplink MC- underlay CRNs based on pricing-game model. The objective of the proposed game model is to maximize the EE utility function and to guarantee the PU' QoS. To fulfil this objective, the authors adopted a linear bandwidth-pricing scheme to improve the efficiency of the NE. Unlike [72], where the authors proposed non-linear pricing scheme, authors in [76] proposed a linear pricing function which reduced the complexity of the optimization problem. Both uniqueness and existence of the NE have been proved mathematically. However, the authors didn't show the convergence of their algorithm in the simulation results. The selfishness scenario has been considered in this work. However, the cheating scenario which considered an important scenario to consider especially in EE paradigm has been ignored. Hence it is not sure how apply the proposed distributed algorithm in more realistic EE scenario.

In addition to the above review, Table 9 summarized the main features of the related studies conducted in the literature to solve the problem of RA in MMC-CRNs with the aid of game and supermarket game theory. This will help the interested readers to memorize the most important components of game/market theory which are: players, strategies and utility function and how these components are related to the objective of the game/market scenario.

Finally, it is worth mentioning that in [43] and [69], the authors provide a comprehensive survey for the application of auction and spectrum leasing in CRNs, respectively, and discuss fundamentals and concepts of supermarket game theory.

6. Open Research Directions

Game and supermarket game theory were proven to be an effective tools in analyzing the problem of resource allocation in MMC-CRNs. However, there are still a number of shortcomings in certain areas where game and supermarket game must attract more attention as follows:

6.1 MC-CR relay game networks (10): Cooperative communication with the aid of relay nodes in MC-CRNs has been recently acknowledged as a promising technology in dynamic spectrum sharing because of the assured enhancement in the performance of both CRs and PUs by providing flexible and efficient resource allocation among all the residents (i.e., players) in a given network. Research on MC-CR relay networks has recently been conducted in the literature, see for example, [79]-[81]. However, extensive studies have not been conducted on the problem of resource allocation in MC-CR relay networks using the concept of game and supermarket game theory. Thus, the problem of resource allocation in MC-CR relay networks remains an open issue that must be addressed.

6.2 Multi-cell MC-CRNs: Most of the studies in the literature focused on single-cell scenarios to address the problem of subcarrier and power allocations among players caused by the simplicity associated with single cell scenario. However, to provide a more practical scenario for real applications, multi-cell scenarios should be considered. Game theory and supermarket game theory can be adopted to facilitate the scenario of multi-cell MC-CRNs in the following proposed scenario: (i) Network-user game/market: In this scenario, the network has the opportunity to select good players that follow the network renting policies (i.e., renting spectrum with minimal interference to PUs) while punishing the players with high spectrum renting prices. (ii) User-network game/market: In this scenario, the users have the opportunity to choose the network that offers a good commodity with a good QoS.

6.3 CRNs over 4G networks: Cognitive radio has become one of the most recognized technologies in 4G networks, e.g., Long Term Evolution Advanced (LTE-A), to solve the spectrum insufficiency problem [8]. OFDM, in contrast, is chosen as the PHY air interface for 4G downlink transmissions because of its promising advantages in providing proper performance and flexibility in allocating spectrum. Thus, adopting game theory and supermarket game theory in the problem of resource allocation in MC-4G-based cognitive radios can be an interesting direction of future study.

6.4 Green Spectrum-Market Game: Research on green technology wireless networks has received significant amounts of attention recently and has become a very important area of investigation for the improvement of the energy efficiency (EE) of networks. In fact, a number of researchers investigated the problem of resource allocation in EE-MMC-CRNs (see, for example, [82]). However, the application of game theory and supermarket game theory to the problem of resource management in MC-Green-CRNs is ignored in recent studies, and a significant amount of effort is needed in this significant field of research. Game theory and supermarket game theory play important roles in designing green CRNs. By applying game theory and supermarket game theory, CR nodes can avoid transmission on certain spectrum that is frequently used by PUs. Furthermore, a green spectrum market can be achieved by applying intelligent supermarket game theory, where CRs incorporate a wide variety of activities, including renting the vacant spectrum wisely by informing other CRs about renting policies (e.g., pricing) so that CRs have the ability to rent spectrum holes that provide minimal interference to nearby PUs. Moreover, by applying a green spectrum market, the CRs can change their expense behavior by buying from good sellers that offer reasonable price for the available spectrum with a good QoS.

7. Conclusion

Game theory and supermarket game theory have become promising tools for modeling and analyzing the interactions of CRs in the context of resource allocation problems in CRNs. In this article, we have presented a comprehensive tutorial on the concepts and applications of "game theory" and "supermarket game theory" to the problem of resource allocation in MMC-CRNs. The game model, in this article, is categorized based on the behavior and interactions among CRs and PUs as non-cooperative, cooperative and supermarket games. In addition, a set of definitions, examples and scenarios related to each model were presented in this tutorial to facilitate an understanding of the concepts of game and supermarket game theory accordingly. The similarities between the behavior of players in MMC-CRNs and the interactions among people in a real market make supermarket game theory better suited to analyze the spectrum trading in MMCCRNs. However, research on the applications of game and supermarket game theory in MMUCRNs remains in its infancy, and more problems must be investigated properly. Finally, we hope that this tutorial will provide important information for interested researchers in the areas of game and supermarket game theory.

http://dx.doi.org/10.3837/tiis.2014.11.003

Appendix

Appendix I: MMC-CRNs interference' mathematical formulation

In equation (1) we have showed the generated interference from CRs-to-PUs in side-by-side spectrum allocation. In addition to eq. 1, there is another amount of interference that generated from PUs-to-CRs which can be defined and modelled according to

Definition 10 [19-21]: interference generated by l-th PU to the
n-th OFDM subcarrier occupied by k-th CR denoted by
[I.sup.CR.sub.l,k] can be defined as the integration of the PSD of
the l-th PU across the n-th subcarrier.

Mathematically speaking the interference introduced by PU's signal
can be modeled according to

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [[phi].sup.PU.sub.k] (f) is the PSD of the l-th PU and
[g.sup.CP.sub.k] is the channel gain of the interference link from
the PUBS to the k-th CR on the n-th subcarrier.


8. Acknowledgements

The authors are very appreciative to the Universiti Kebangsaan Malaysia and Malaysia's Ministry of Higher Education (ERGS/1/2013/ICT03/UKM/02/1) for funding of this work. The authors would also like to thank the editor and the anonymous reviewers for their valuable feedback.

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Omar B.Abdul-Ghafoor (1), Mahamod Ismail (1), Rosdiadee Nordin (1), Musbah M. R. Shaat (2)

(1) Department of Electrical, Electronic and System Engineering, University Kebangsaan Malaysia, Bangi, Malaysia

[e-mail: omar.omarghafoor@gmail.com], [mahamod@eng.ukm.my], [adee@eng.ukm.my]

(2) Centre Tecnologic de Telecomunicacions de Catalunya (CTTC), Barcelona - Spain [e-mail: musbah.shaat@cttc.es]

Corresponding author: Omar B. Abdulghafoor

Received April 30, 2014; revised July 8, 2014; accepted July 21, 2014; published November 30, 2014

(1) The first point (i.e., spectrum sensing technique) is beyond the scope of this tutorial article.

(2) Please refer to [16] for a comprehensive tutorial on OFDM and FBMC.

(3) Please refer to appendix-I for details on interference' mathematical formulation.

(4) Please refer to [26] for more details on the concept of pure strategy game, mixed strategy game and correlated equilibrium (CE)

(5) Please refer [33] for additional details about potential game.

(6) Please refer to [34] for additional details about the standard function and uniqueness of NE.

(7) Please refer to [37] definition 2 for addition details about the Nash bargaining intuitive axioms

(8) Please refer to [41] for a comprehensive survey on coalition game and the definition of its categories.

(9) Please refer to [29] for an example on how pricing method plays an important role in providing efficient NE.

(10) Please refer to [78] for examples of the application of game theory to interference coordination in OFDMA relay networks.

Omar B. Abdulghafoor is a Ph.D. candidate in the Department of Electrical, Electronics and System Engineering, Universiti Kebangsaan Malaysia (UKM). He received his B.Sc. in Control and Computer Eng. from University of Technology, 2001 and the MEng. in Computer and Communication from Universiti Kebangsaan Malaysia in 2005. His research interests include cognitive radio, wireless communications, resource allocation and game theory applications.

Mahamod Ismail joined the Department of Electrical, Electronics and System Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia (UKM) in 1985, and currently, he is a Professor in Communication Engineering. He is also appointed as the Deputy Director (Education and Research) Centre of Information Technology, UKM. He received the B.Sc. degree in Electrical and Electronics from University of Strathclyde, U.K. in 1985, the M.Sc. degree in Communication Engineering and Digital Electronics from University of Manchester Institute of Science and Technology (UMIST), Manchester U.K. in 1987, and the Ph.D. from University of Bradford, U.K. in 1996. He was with the first Malaysia Microsatellite TiungSat Team Engineers in Surrey Satellite Technology Ltd. U.K. for 9 months started in June 1997. His research interests include mobile and satellite communication as well as wireless networking, particularly, on the radio resource management for the next generation wireless communication. He also published more than 300 technical publications in local and international conferences and journals. He is an active member in professional bodies such as Institute of Electrical and Electronics Engineers (IEEE), USA and Malaysia Society of Engineers and Technologist (MSET) and currently the Vice Chair of IEEE Malaysia Section and executive committee member for Joint Communication and Vehicular Technology Society Chapter IEEE Malaysia.

Rosdiadee Nordin received his B.Eng. from Universiti Kebangsaan Malaysia in 2001 and Ph.D. from University of Bristol, United Kingdom in 2011. He is currently a senior lecturer in Department of Electrical, Electronics and System Engineering in Universiti Kebangsaan Malaysia. His research interests include resource allocation, green radio, Multiple-Input Multiple-Output (MIMO), Orthogonal FrequencyDivision Multiple Access (OFDMA), carrier aggregation (CA), cognitive radio and indoor wireless localization.

Musbah M Shaat obtained his engineering degree major in communication and control from the Electrical and Computer Engineering Department at the Islamic University of Gaza (IUG), Palestine (1999-2004). He worked for one year (20042005) as full time teaching assistant at the electrical engineering department at the IUG. He awarded the DAAD "German Academic Exchange Service" master scholarship and got the master degree in communication and electronics engineering from Jordan University of Science and Technology (JUST), Jordan (2005-2007). He obtained his PhD degree from the Signal Theory and Communication department (TSC) at the Polytechnic University of Catalonia (UPC), Spain (2007-2012). He worked as a research associate in the Access Technologies Area in Centre Tecnologic de Telecomunicacions de Catalunya (CTTC)-Spain until he joined the electrical engineering department at the Islamic university of Gaza in September 2012.

Table 1. Main Components of the CRN Models.

Architecture              Component

Infrastructure approach   1. Primary user base station (PUBS):
                          Coordinate licensed spectrum bands for
                          PUs' usage.

                          2. PUs: Ordinary mobile nodes, which are
                          known as the owner of the spectrum, that
                          have higher priority to use the
                          available band.

                          3. Cognitive radio base station (CRBS):
                          Coordinate the coexistence of CRs and
                          PUs in licensed spectrum.

                          4. CRs/SUs: Cognitive radio users or
                          secondary users that perform a spectrum
                          sensing technique to utilize the vacant
                          bands.

Ad-hoc approach           1. Primary user base stations (PUBs): As
                          defined above.

                          2. PUs: As defined above.

                          3. CRs/SUs: Communicate in an ad-hoc
                          fashion.

                          4. CRBS: Not available in the ad-hoc
                          approach.

Table 2. Comparison of player behavior in a non-cooperative game4.

Game Model            Description                 Type of Equilibrium

Pure strategy game    A normal or strategic       Nash equilibrium
                      game is considered the      (NE)/correlated
                      basic model in game         equilibrium (CE)
                      theory. The players, in
                      this case, are assumed to
                      carry out only
                      deterministic strategies
                      (called pure

Mixed strategy game   In a mixed strategy game,   Mixed strategy Nash
                      the actions of the          equilibrium
                      players are described by
                      probability
                      distributions.

Table 3. Link between Game' component and the elements of MMC-CRNs

Basic Component of Game   Equivalent MMC-CRN' Elements

Players                   Players are the cognitive nodes
                          available in the network

Strategy Space            Strategy space, according to scenario_1,
                          is the subcarriers left over by the PUs.

Utility Function          The utility function depends on the
                          network setting and it may be
                          maximization of throughput or
                          minimization of some cost function in
                          order to mitigate the generated
                          interference to the owner of the
                          spectrum.

Table 4. Mapping of auction theory elements to MC-CRNs.

Auction Component Bidders   Comments Bidders are   Element of MC-CRN In
                            the buyers (auction    MMC-CRNs, the buyers
                            players) who want to   are CR nodes. Buyers
                            buy resources for      compete with each
                            their transmission.    other to obtain
                                                   certain resource for
                                                   transmission
                                                   matters.

Seller                      The seller is the      In MMC-CRNs, the
                            owner of the radio     seller is a PUs/PUBS
                            resource (auction      that holds the
                            player) who wants to   license to use the
                            sell unused            available spectrum.

Auctioneer                  A midway agent         In MMC-CRNs, the
                            between bidders and    auctioneer can be
                            sellers who control    the seller (e.g.,
                            the auction's          PUBS or PUs).
                            process.

Commodity                   The commodity or       In MMC-CRNs, the
                            auction commodity is   commodities are, for
                            the product traded     example, the vacant
                            among buyers and       subcarriers.
                            sellers.

Table 5. Different types of oligopoly games.

Game                        Key Features                  Example

Cournot       * Firms make their decisions
              simultaneously.

              * Single commodity produced by n firms.

              * The actions of firms affect other        [48], [49]
              firms in the market because the price
              depends on the overall quantity.

Bertrand      * Firms' actions are performed                [50]
              independently and simultaneously in
              terms of price.

              * Firms' decisions are strategic
              variable prices instead of quantities
              output.

Stackelberg   * Firms choose their quantities
              sequentially.

              * Leader-follower approaches: Because         [51]
              the decisions of firms are sequential,
              the firm that produces his offer first
              is called the leader, and the others are
              followers that take into account the
              leader's decisions to make their own
              decisions.

Table 6. Details of applications' classes

Class Type   Class description             Sub-class description

A            Research type                 A.1: Technical research
                                           A.2: Survey research

B            Cognitive and non-cognitive   B.1: Cognitive scenario
               scenario
                                           B.2: Non-cognitive scenario

C            Resource allocation           C.1: Rate-adaptive game
               approaches                  C.2: Margin-adaptive game
                                           C.3: General Approach

D            Cell model                    D.1: Single-cell scenario
                                           D.2: Multiple-cell scenario

E            Network model                 E.1: Centralized model
                                           E.2: Distributed model

Table 7. A summary of related studies on the applications of game and
supermarket game theory in multicarrier techniques.

Ref.   Game Model                                 Class

                                          A                   B

                                 A.1       A.2       B.1       B.2

[43]   Auction-Game                        [check]   [check]

[59]   NCGT                      [check]                       [check]
[60]   Market-Game               [check]             [check]
[62]   Auction-Game              [check]                       [check]
[63]   CGT                       [check]                       [check]
[64]   NCGT                      [check]             [check]
[65]   NCGT                      [check]                       [check]
[66]   NCGT                      [check]                       [check]

[67]   Potential-NCGT            [check]             [check]
[68]   Market-Game               [check]             [check]

[69]   Market-Game                         [check]   [check]

[70]   Stochastic- Market-Game   [check]                       [check]
[71]   Auction-Game              [check]                       [check]
[72]   NCG-Pricing               [check]             [check]
[73]   NCG-Colonel Blotto-Game   [check]             [check]
[74]   Market-Game               [check]             [check]

[75]   Stackelberg-Market Game   [check]             [check]

[76]   NCGT                      [check]             [check]

[77]   Oligopoly Market          [check]             [check]

Ref.   Game Model                            Class

                                               C

                                 C.1       C.2       C.3

[43]   Auction-Game                                  [check]

[59]   NCGT                                [check]
[60]   Market-Game                                   [check]
[62]   Auction-Game              [check]
[63]   CGT                       [check]
[64]   NCGT                      [check]
[65]   NCGT                      [check]
[66]   NCGT                      [check]

[67]   Potential-NCGT            [check]
[68]   Market-Game               [check]

[69]   Market-Game                                   [check]

[70]   Stochastic- Market-Game   [check]
[71]   Auction-Game              [check]
[72]   NCG-Pricing               [check]
[73]   NCG-Colonel Blotto-Game   [check]
[74]   Market-Game                                   [check]

[75]   Stackelberg-Market Game   [check]

[76]   NCGT                      [check]

[77]   Oligopoly Market                              [check]

Ref.   Game Model                                 Class

                                         D                   E

                                 D.1       D.2       E.1       E.2

[43]   Auction-Game              [check]             [check]   [check]

[59]   NCGT                      [check]                       [check]
[60]   Market-Game               [check]             [check]
[62]   Auction-Game              [check]   [check]   [check]   [check]
[63]   CGT                       [check]             [check]
[64]   NCGT                                [check]   [check]
[65]   NCGT                      [check]             [check]
[66]   NCGT                      [check]   [check]   [check]

[67]   Potential-NCGT            [check]                       [check]
[68]   Market-Game               [check]             [check]

[69]   Market-Game               [check]             [check]   [check]

[70]   Stochastic- Market-Game   [check]             [check]
[71]   Auction-Game                        [check]   [check]
[72]   NCG-Pricing               [check]                       [check]
[73]   NCG-Colonel Blotto-Game   [check]             [check]
[74]   Market-Game                         [check]             [check]

[75]   Stackelberg-Market Game   [check]                       [check]

[76]   NCGT                      [check]                       [check]

[77]   Oligopoly Market          [check]             [check]

Ref.   Game Model                     Game Solution

[43]   Auction-Game              * Game-Solutions:
                                 different solutions can
                                 be provided in auction
                                 game according to
                                 auction design such as:
                                 NE, mixed-strategy
                                 equilibrium, correlated
                                 equilibrium (CE)

[59]   NCGT                      * Game-Solution: NE
[60]   Market-Game               * Game-Solution: NE
[62]   Auction-Game              * Game-Solution: NE
[63]   CGT                       * Game-Solution: NBS
[64]   NCGT                      * Game-Solution: NE
[65]   NCGT                      * Game-Solution: CE
[66]   NCGT                      * Game-Solution: NE in
                                 Potential game
[67]   Potential-NCGT            * Game-Solution: NE
[68]   Market-Game               * Game-Solution: different
                                 solutions depending on
                                 market setup.
[69]   Market-Game               * Game-Solution: different
                                 solutions depending on
                                 market setup.
[70]   Stochastic- Market-Game   * Game-Solution: NE
[71]   Auction-Game              * Game-Solution: NE
[72]   NCG-Pricing               * Game-Solution: NE
[73]   NCG-Colonel Blotto-Game   * Game-Solution: NE
[74]   Market-Game               * Game-Solution: NE with
                                 pricing
[75]   Stackelberg-Market Game   * Game-Solution: NE with
                                 pricing
[76]   NCGT                      * Game-Solution: NE with
                                 pricing
[77]   Oligopoly Market          * Game-Solution: NE with
                                 pricing

Table 8. Main features for RA in MC-wireless scenarios.

[ ]         Objective           Players          Strategies

[59]       Reduce power          Nodes      Players to allocate
        consumption of the                       power and
       network and satisfy                      subcarrier.
        the target rate on
        each subcarrier in
        OFDM networks via
              NCGT.

[63]    Efficient and fair       Nodes      Players to allocate
       RA in multiuser OFDM                      power and
         networks through                       subcarrier.
               CGT.

[65]     Energy efficient     Subcarriers      Subcarriers to
       (EE) RA in OFDMA to                      choose most
           balance the                       satisfying users.
        trade-off between
           total energy
          efficiency and
        fairness via NCGT.

[66]   Fast, distributed RA      Nodes       Players to select
        in OFDMA networks                        power and
        via potential NCG.                      subcarrier.

[70]    Fast, distributed,       Nodes       Players to select
        joint RA algorithm                       power and
         in uplink OFDMA                        subcarrier.
           networks via
          potential NCG.

[71]     Efficient RA in      Nodes and      Nodes' strategies:
          combinatorial          base       subcarrier and power
         auction game in       stations       allocation. BSs'
         multi-cell OFDMA        (BS)       strategies: setting
            networks.                        the price for the
                                                 commodity.

[ ]        Payoffs and
           Constraints

[59]      Cost function:
            Minimizing
        transmitted power
         subject to local
          power and rate
           constraints.

[63]   BG utility function:
       Maximize bargaining
         utility function
        subject to power,
         rate and channel
           constraints.

[65]   Logarithmic utility
       function: Maximizing
       EE utility function
         subject to power
           constraints.

[66]      Cost function:
        Maximizing surplus
       function subject to
        power constraints.

[70]      Cost function:
        Maximizing surplus
       function subject to
          maximum power

           constraints.

[71]      Cost function:
            Minimizing
        transmitted power
         subject to local
         power, rate and
       channel constraints.

Table 9 Main features for RA in MC-wireless scenarios.

[ ]         Objective            Players           Strategies

[61]        Efficient,            CRs:           CRs: providing
           cooperative          bidders       relaying service to
         communication in         PUs:         PUs. PUs: leasing
          OFDM spectrum        auctioneer       vacant band as a
         monopoly leasing                          revenue of
              market                           cooperation to the
                                                      CRs

[64]     RA algorithm in          CRBS        CRBS: choosing power
       multi-cell multiuser                    on different bands
       uplink scenarios in                    for their own users
            FBMC CRNs                                (CRs)

[67]       Interference           Nodes           Subcarriers
           minimization                            selections
        algorithm in OFDMA
               CRNs

[68]     Spectrum leasing         CRs:           CRs: providing
        market for better       bidders       relaying service to
       spectrum utilization       PUs:        PUs. PUs: selecting
          in OFDMA CRNs        auctioneer        best relaying
                                                    services

[72]       Distributed,           Nodes       Allocating power on
       noncooperative power                     subcarriers with
        allocation in FDMA                    less interference to
               CRNs                                   PUs

[73]   Joint subcarrier and   Bidders (CRs)     Power and budget
       power allocation in                         allocation
          OFDMA CRNs via
          Colonel Blotto

[74]   Competitive spectrum     Service         Sellers: attract
         supermarket with      providers      potential consumers.
          dynamic prices      (sellers) and        Consumers:
                                 nodes          evaluating (and
                                (buyers)       selecting) sellers
                                                   with good
                                                 applications,
                                                   operating
                                                technologies and
                                                    location

[76]     Energy-Efficient          CRs        Joint subcarrier and
          (EE) resource                         power allocation
       allocation in OFDMA
        CRNs with pricing
               game

[ ]        Payoffs and
           Constraints

[61]   CRs: Maximize profit
          function as a
       function of revenue
       that can be obtained
          and the power
         consumed in the
       cooperation process.
        PUs: Maximize its
       date rate by getting
       more relay services
            from CRs.

[64]        Maximizing
       information rate for
       each CRBS subject to
         interference and
        power constraints.

[67]      Potential game
         utility function
            subject to
       interference, power
          and subcarrier
           constraints

[68]     Maximizing rate
       function subject to
       power, interference
       and QoS constraints.

[72]      Cost function:
        maximizing surplus
       function subject to
          maximum power,
         interference and
       channel constraints.

[73]     Utility function
        subject to power,
            budget and
           interference
           temperature
           constraints.

[74]   Dynamic pricing for
            price-and
        quality-sensitive
       customers. Moreover,
          sellers group
        against others to
          increase their
             revenue.

[76]    Utility function:
         maximize the EE
         utility function
       subject to bandwidth
            and power
           constraints
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Author:Abdul-Ghafoor, Omar B.; Ismail, Mahamod; Nordin, Rosdiadee; Shaat, M.R. Musbah
Publication:KSII Transactions on Internet and Information Systems
Article Type:Report
Date:Nov 1, 2014
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