# Ultrabroadband competition from a 2-sided market perspective.

There are an increasing number of 2-sided markets in today's economy, with continuous development of innovative business models in almost all industries. Due to inter-market externality, pricing strategies by the intermediate platform often differ quite substantially from traditional thinking, and the area has begun to gain long deserved attention from the research community in the recent years. Contributions have been from CORTADE (2006), ECONOMIDES & KATSAMAKAS (2006), ECONOMIDES & TAG (2007), FARHI & HAGIU (2007), PARKER & VAN ALSTYNE (2005), ROCHET & TIROLE (2003, 2006), ROOS (2007), and ROSON (2005), to name a few. Yet, there still remains some ambiguity as for competitive strategies, and this will be the subject of this article with a focus on the Internet Service Provider (ISP) as the intermediate platform.The ISP serves a 2-sided market, with general subscribers on one side and contents providers on the other. There is significant inter-market externality between the two markets, with on-going evolution of the contents industry and ISPs' exponentially growing transmission capabilities to accommodate heavier traffic. With demand for higher capacity contents from general subscribers continuously on the rise, this inter-market dependency, which is the main characteristic of the 2-sided market model, will become much stronger as we develop into the Ultrabroadband (UBB) era, defined as 1Gbps or more of subscriber capacity. The UBB era internet would be a truly revolutionary value creating medium from business as well as socio-economic perspectives, and futuristic contents would most likely change lifestyles of the majority.

The objective of this article is to better understand and develop strategies for ISP competition in the UBB era using the 2-sided market model. An overview of the model is presented and a Cournot-Nash Equilibrium under 2-sided market duopoly competition is derived. This leads to the final section, where an analysis of competitive strategies for firms under inter-market externality conditions is provided in terms of the quantity variable.

* 2-sided market

A 2-sided market is best described by market demands on both sides of the firm being influenced by each other. The diagram in figure 1 below explains this with F representing the ISP. C represents the general consumer (subscriber) market and A represents the applications (or contents) market. D.(p.) denotes the no-externality demand function of price p. for market i. It is the demand of market i regardless of any effect from market j. Internetwork externality [e.sub.ij] measures the effect of market i on market j. Denoting [q.sub.i] as the overall demand for market i accounting for internetwork externality, we have the following linear model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [1]

Assuming negligible marginal cost, profit for the firm:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Let [bar.p] and [??] denote the optimal price (profit maximizing) coordinated across both markets and independently applied for each market, respectively. In general, [bar.p] [not equal to] [??] unless [e.sub.AC]= [e.sub.CA]=0. The coordinated profit maximizing pricing scheme could be such that the firm operates at a suboptimal point on one side of the market in order to gain higher profit on the other side, thus reaching an optimal solution from an overall perspective. Simple examples are free "Adobe Readers" and free "ladies admission" to nightclubs as illustrated in figure 2. The subsidized side contributes to the overall profit through raising demand on the other side, where the firm would be able to obtain higher profit.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

In order to gain some insight into 2-sided market properties, we present some results from PARKER & VAN ALSTYNE (2005) without proof.

Result 1: If [partial derivative][q.sub.A]/ [partial derivative][p.sub.C] = [partial derivative][q.sub.C]/ [partial derivative][q.sub.A], then [??] [less than or equal to] [??]. That is, independent profit maximizing leads to equal or higher prices in both markets.

Result 2: Consumer surplus is equal or higher in the coordinated case than in the independent case for both markets. Also, [bar.[pi]] [greater than or equal to] [??], trivially. Thus, social welfare should improve under the firm's coordinated pricing across both markets as compared to the case where two separate firms each deal exclusively with a single market on opposite sides and price independently.

The second result regarding consumer surplus might sound somewhat counterintuitive from a traditional market structure perspective, and explains that the coordinated monopoly firm is not able to reap the entire extra surplus created by inter-market externality.

The 2-sided market properties become much more complex when faced with competitive strategies for firms. Notable references on duopoly competition are ECONOMIDES & TAG (2007) and ROCHET & TIROLE (2003). Both papers derive noncooperative optimal solution for profit maximization based on the price variable. However, the underlying 2-sided demand models are rather complex (location and probabilistic, respectively), and it is not clear whether the derived optimal solution is stable in a Nash equilibrium sense. In the following section we develop a Nash equilibrium solution based on the quantity variable under a simple 2-sided demand structure.

* Cournot-Nash equilibrium

We can express the 2-sided market demand as follows:

[q.sub.C] = a - b[p.sub.C] - e[p.sub.A] [2] [q.sub.A] = C - d[p.sub.A] - e[p.sub.C]

where [q.sub.i] and [p.sub.i] are quantity and price variables, respectively, as previously discussed in [1]; a, b, c, d and e are nonnegative constants; and b, d > e since the price effect should surely be higher within than across the markets. Notice that the internetwork externality factor e has now been assumed to be identical in both directions.

The expression in [2] can be rearranged using renamed nonnegative constants A, B, C, D and E as:

[p.sub.c] = A - B[q.sub.c] + E[q.sub.A]

[p.sub.A] = C - D[q.sub.A] + E[q.sub.c] [3]

where B, D > E. Note that E is now the internetwork externality factor in the rearranged system. To ensure A, C [greater than or equal to] 0, we need to assume ad [greater than or equal to] ce and cb [greater than or equal to] ae in [2], which would require slightly more than the given conditions of b, d > e. The assumption would be quite realistic considering that the demand functions describing the two markets should reasonably resemble each other, placing a and c not too far apart in value. Derivation of [3] from [2] with B, D > E is outlined in the appendix. Our work will proceed based on the system in [3] to arrive at a Cournot-Nash equilibrium for two competing firms with quantity as the decision variable.

Consider Firms 1 and 2 competing for the 2-sided market. The market quantity variables can be expressed as follows:

[q.sub.c] = [q.sup.1.sub.c] + [q.sup.2.sub.c]

[q.sub.A] = [q.sup.1.sub.A] + [q.sup.2.sub.A]

where [q.sup.j.sub.i] represents market i demand for firm j. The situation is depicted in figure 3 below.

[FIGURE 3 OMITTED]

Now we develop a Cournot-Nash Equilibrium. To do so, we optimize the profit function in terms of the quantity variable. Assuming negligible marginal cost, profit for Firm 1, which is concave (proof of concavity is provided in the appendix) in [q.sup.1.sub.c] and [q.sup.1.sub.A] is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [4]

First order necessary conditions are:

[partial derivative] [[pi].sup.1]/[partial derivative] [q.sup.1.sub.c] = [partial derivative] [[pi].sup.1] /[partial derivative] [q.sup.1.sub.A] = 0,

producing best response functions:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

which, upon letting [q.sup.1.sub.C] = [q.sup.2.sub.C] and [q.sup.1.sub.A] = [q.sup.2.sub.C] due to the symmetric nature of the model, leads to the 2-sided Cournot-Nash equilibrium:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [5]

* Analysis of firm strategy

As discussed above, coordinated pricing across the two markets would generate higher social welfare as well as the (monopoly) firm's profit than in the case of independent pricing. But how would independent pricing by two separate firms each dealing exclusively with a single market on opposite sides (hereto after referred to as "split markets") compare to the 2-sided market duopoly discussed in section III in terms of profit? This will be explored in the current section with continued assumption of negligible marginal cost.

We first look at the monopoly and duopoly profits. Using equation [3], the monopoly firm's profit can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [6]

which is concave in [q.sub.C] and [q.sub.A] (proof of concavity is very similar to the one in the appendix). Using first order necessary conditions:

[partial derivative] [pi]/[partial derivative] [pi] = [partial derivative] [q.sub.C] /[partial derivative] [q.sub.A] = 0,

we obtain the following optimal quantity values:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [7]

Substituting [7] into [6], optimal monopoly profit can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [8]

Using [5], the duopoly Cournot-Nash equilibrium profit for Firm 1 is as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Profit for Firm 2 should be the same, and the combined Cournot-Nash profit for the two firms is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

which is naturally smaller than the monopoly profit [??] expressed in [8].

Now, we look at the "split markets" case described above. Without loss of generality, Firm 1 would focus on the consumer market C only and Firm 2 on the applications market A only. Figure 4 depicts the situation.

[FIGURE 4 OMITTED]

Using equation [3] and omitting the superscript for the quantity variables, profit for the firms can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [10]

which are concave in [q.sub.C] and [q.sub.A], respectively (proof of concavity is trivial here). Using first order necessary conditions:

[partial derrivative] [[pi].sup.1] / [partial derrivative] [q.sub.C] = [partial derrivative] [[pi].sup.2] /[partial derrivative] [q.sub.A]

we obtain the following respective optimal quantity values:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [11]

Substituting [11] into [10], optimal profit for the firms can be expressed

as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Combined profit is then:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [12]

Since the monopoly firm always has the option to face the two markets independently, [bar.[pi]] [greater than or equal to] [??]. Notice that with E = 0 (zero inter-market externality in [3]), expression in [12] becomes equal to that of the monopoly profit in [8]. This is natural since zero inter-market externality, by definition, indicates that the two markets are independent.

We are now ready to compare the "split markets" with the 2-sided duopoly. We ask the question, "wouldn't two firms be better off splitting the markets rather than engaging in 2-sided duopoly competition?" We investigate this under the following framework where [??] is expressed in a form that would facilitate making comparison to [bar.[pi]] and [[pi].sub.CN] under different inter-market externality conditions. For any given set of nonnegative values for A, B, C and D, define r(E) as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [13]

Notice the term inside the parenthesis appearing in common in both the expressions in [8] and [9] for the cases of monopoly and Cournot-Nash duopoly, respectively. Then the following observations can be made. Firstly, [??] = [bar.[pi]] for E = 0, as stated above, and thus, r(0) = 1/4. Secondly, if there exists an [E.sub.CN] > 0 such that r([E.sub.CN])=2/9, then [??] = [[pi].sub.CN] at E = ECN. However, the existence might depend on the given set of values for A, B, C and D, and we will not make efforts to provide a rigorous analysis here. However, for practical purposes we state the following lemma, the proof of which is provided in the appendix.

Lemma: Given a set of nonnegative values for A, B, C and D, r(E) is strictly decreasing in E for E > 0.

Thus, whether r(E) reaches down to the 2/9 mark or not, the strategic implication is that given a set of values for A, B, C, D and E, if r(E) >2/9, then "split markets" would the better choice; otherwise, the Cournot-Nash equilibrium should be the competitive strategy. Table 1 below illustrates this from the combined profit perspective. The result is quite intuitive in that, for example, the Cournot-Nash would the strategic choice with smaller r(E), i.e. larger inter-market externality factor E. Loss from competition would be more than compensated through efforts coordinated across the markets in reaping the surplus created through larger intermarket externality. The significance here is the critical point r (E) =2/9 for the right strategic choice.

When we state that the "split markets" is the better choice, we mean [??] > [[pi].sub.CN], where [??] is the combined profit for the two firms each engaging exclusively in the opposite sided markets. However, unless A = C and B = D (the demand curve being identical in the two markets), profit would differ across the two markets, and which of the firms would take the more profitable side becomes a question. Adding to this complexity, profit under the "split markets" can be higher or lower than under the Cournot-Nash equilibrium for the firm taking the less profitable market.

In any case, both markets will have to be served by nature of the 2-sided market, and from a noncooperative equilibrium perspective, the Cournot-Nash strategy would be the only stable solution since neither firm would want to miss the opportunity provided by either of the markets. In other words, under any split market scenario, a firm engaging with one market would decide to enter the other side as well, since it can only gain by doing so. The problem is that the other firm would do the same, which would inevitably result in both firms targeting both markets.

One way the [??] > [[??].sub.CN] situation can work to benefit the firms would be under peering and transit arrangements between the two, which is necessary after all for connecting traffic between subscribers to the different firms. These arrangements may serve as creative mechanism for compensating the firm with the less profitable side, allowing for realistic implementation of the "split markets" strategy, as shown in figure 5.

[FIGURE 5 OMITTED]

* Conclusion

We have derived a duopoly Cournot-Nash equilibrium under the 2-sided market environment, made an analysis of the "split markets" situation in comparison to the monopoly regime on one hand and Cournot-Nash on the other, and finally suggested strategies for competing firms.

Further research on 2-sided markets should produce valuable insights into the otherwise counterintuitive framework. Present and future results from the 2-sided market model should not only be well understood by platform firms in forming optimal business strategies, but also by policy makers and regulatory bodies since seemingly straightforward initiatives can often run counterproductive under this new and rather complex setting.

Appendix

A. Derivation of system [3] from system [2]

System [2] expresses quantities in terms of prices as follows:

[q.sub.C] = a - [bP.sub.C] - [ep.sub.A]

[q.sub.A] = c - [dP.sub.A] - [ep.sub.C]

By multiplying d and e to the first and second equations, respectively, and then subtracting the second from the first we obtain:

dqC--eqA = pC (e2--bd) + (ad - ce)

Rearrangement leads to:

[p.sub.C = (ad - ce)/(bd - [e.sup.2]) - d/(cd - [e.sup.2]) [q.sub.c] + e/(bd - [e.sup.2]) [q.sub.A]

In a similar fashion we may obtain:

[p.sub.A] = (cb - ae)/(bd - [e.sup.2]) - b/(bd - [e.sup.2]) [q.sub.A] + e/(bd - [e.sup.2]) [q.sub.C]

Now, to have the above two equations well express price as function of demand, we need the assumptions ad [greater than or equal to] ce and [c.sub.b] [greater than or equal to] ae. Then, we may express the equations as in system [3]:

[p.sub.C] = A - [Bq.sub.C] + [Eq.sub.A]

[P.sub.A] = C - [Dq.sub.A] + [Eq.sub.C]

with nonnegative constants A, B, C, D and E. Since b, d > e, we have

B, D > E as well.

B. Proof of concavity of profit function in [4], the duopoly case

Profit function for firm 1:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

To prove that [[pi].sup.1]([q.sup.1.sub.C], [q.sup.1.sub.A], [q.sup.2.sub.C], [q.sup.2.sub.A]) is concave in ([q.sup.1.sub.C], [q.sup.1.sub.A]), the variables under firm 1's control, we show that the corresponding Hessian is negative semidefinite:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

C. Proof of Lemma: Given a set of nonnegative values for A, B, C and D, r(E) is strictly decreasing in E for E [greater than or equal to] 0.

From [12] and [13] we have

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Thus,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Now, comparing the terms in the numerator of the last expression above, we realize that for E > 0,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

implying [partial derivative]r(E)/ [partial derivative]E < 0 for E > 0. Since [partial derivative]r(E)/ [partial derivative]E [|.sub.E=0] 0, r(E) is strictly decreasing in E for E [greater than or equal to] 0.

Bibliography

CORTADE T. (2006): "A Strategic Guide on Two-Sided Markets Applied to the ISP Market", COMMUNICATIONS & STRATEGIES, no. 61, 1st Q., pp. 17-35.

ECONOMIDES N. & KATSAMAKAS E. (2006): "Two-Sided Competition of Proprietary vs. Open Source Technology Platforms and the Implications for the Software Industry", Management Science, vol. 52, no. 7, pp. 1057-1071.

ECONOMIDES N. & TAG J. (2007): "Net Neutrality on the Internet: A Two-sided Market Analysis", NET Institute Working Paper.

FARHI E. & HAGIU A. (2007): "Strategic Interactions in Two-Sided Market Oligopolies", Harvard University Working Paper.

PARKER G. & VAN ALSTYNE M. (2005): "Two-Sided Network Effects: A Theory of Information Product Design", Management Science, vol. 51, no. 10, pp. 1494-1504.

ROCHET J.C. & TIROLE J.:

--(2003): "Platform Competition in Two-Sided Markets", Journal of the European Economic Association, vol. 1, no. 4, pp. 990-1029.

--(2006): "Two-Sided Markets: A Progress Report", Rand Journal of Economics, vol. 37, no. 3, pp. 645-667.

ROOS J. (2007): "Channel Structure in Two-Sided Markets", Working Paper.

ROSON R. (2005): "Two-Sided Markets: A Tentative Survey", Review of Network Economics, vol. 4, issue 2, pp. 142-160.

Beong-geel CHOI

KT Management Research, Korea

Table 1--Strategic choice depending on r(E) r(E) = 1/4 Combined Profit (i.e. E = 0) r(E) >2/9 C-N 2([A.sup.2] D + B[C.sup.2] + x x 2 ACE)/9(BD - [E.sup.2]) Split r(E)([A.sup.2]D + B[C.sup.2] + Equivalent Strategic mkts 2 ACE)/BD - [E.sup.2] to monopoly choice Combined Profit r(E) <2/9 C-N 2([A.sup.2] D + B[C.sup.2] + Strategic 2 ACE)/9(BD - [E.sup.2]) choice Split r(E)([A.sup.2]D + B[C.sup.2] + x mkts 2 ACE)/BD - [E.sup.2]

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Title Annotation: | Ultrabroadband: the next stage in communications |
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Author: | Choi, Beong-geel |

Publication: | Communications & Strategies |

Date: | Nov 1, 2008 |

Words: | 3186 |

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