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Wage and employment negotiations between a union and a firm in a dynamic context.

I. Introduction

The traditional analysis of union-firm interaction has focused on two static models - the Monopoly Union Model (with its equilibrium on the labor demand curve) and the Efficient Contract Model (with its equilibrium on the efficient contract curve).(1) Espinosa and Rhee [3, 565-88] reconcile these two approaches within the context of a repeated game framework. They show that repeated sequential bargaining (between a union and a firm with the union moving first) may generate the efficient outcome if the firm is sufficiently far sighted. However, if the firm is short sighted, it may unilaterally deviate from the cooperative agreement, to take advantage of a one-period gain. On the other hand, being the first mover, the union never unilaterally deviates from cooperation.

This paper argues that in certain situations the union may also have the incentive to unilaterally deviate from the cooperative outcome. In reality the firm's position is often less flexible than that assumed by Espinosa and Rhee [3]. Based on the long term trust that the union and the firm develop, the firm may undertake commitments in the form of consumer orders, large fixed capital expenditures, expenditures on raw materials and other inputs, and similar other inflexibilities. The union, being aware of the firm's inflexibilities, may hold the firm to its surprise demands for a one-period gain, provided that it is sufficiently short sighted.

Therefore, this paper analyzes a simultaneous move, repeated game model where both the union and the firm have the power to deviate.(2) We analyze the implications of such deviations on the equilibrium paths of wage and employment. The paper shows that cooperation is much harder to sustain when both the union and the firm can deviate as compared to the case where only the firm can deviate. In fact some cooperation is not guaranteed. Cooperation completely breaks down over large ranges of the discount factor and the two parties choose the one-shot non-cooperative Monopoly Union equilibrium. This result is in sharp contrast to the existing literature where some cooperation is feasible for all values of the discount factor, except zero. Therefore ignoring possibilities of union deviation tends to overestimate the possibility of cooperation. Secondly, in the case where the union has a greater inherent tendency to deviate than the firm, the union may be able to get a much better bargain for itself - a higher wage for a given level of employment. This may happen because when the union deviates, allowing a wage hike is a sure way of inducing cooperation from the union. Increasing employment, on the other hand, may have an ambiguous effect.

The rest of the paper is organized in three main sections. Section II presents the model and the analytical results. Section III simulates the model with an example. Section IV concludes.

II. The Simultaneous Game Model

We present below, a simultaneous move, repeated game model featuring two agents - a union and a firm. At every time period t, the union determines the wage and the firm determines the level of employment, simultaneously.

Description of the Functions and Objectives of Agents

The production function for the firm is assumed to be a function of labor (capital is assumed to be in place) and is given by:

[Q.sub.t] = F([L.sub.t]); F[prime] [greater than] 0, F[double prime] [less than] 0, for all t, (1)

where, [Q.sub.t] is the output of the firm at time t and [L.sub.t] is the level of employment at time t. Therefore the profit equation of the firm is given by:

[Pi]([w.sub.t], [L.sub.t]) = V(F([L.sub.t])) - [w.sub.t][L.sub.t]; V[prime] [greater than] 0, V[double prime] [less than or equal to] 0, (2)

where V is total revenue as a function of output and [w.sub.t] is the wage rate at time t. Notice that V[double prime] [less than or equal to] 0 is sufficient for the Marginal Revenue Product of labor curve to be downward sloping. Profit maximization yields the firm's labor demand curve as:

[Mathematical Expression Omitted],

where [Mathematical Expression Omitted] is the labor demand at time t. [L.sup.*] ([w.sub.t]) is implicitly derived from first order condition of profit maximization [V[prime] ([center dot]) F[prime] ([center dot]) = [w.sub.t]]. The objective of the firm is to choose employment so as to maximize the present discounted value of the infinite stream of future profits.

Following the traditional economic theory of the trade union, the union is assumed to comprise of identical members and maximize the following well behaved utility function:

U ([w.sub.t], [L.sub.t]); [U.sub.w] [greater than] 0, [U.sub.L] [greater than] 0, (4)

where [w.sub.t] and [L.sub.t] are as defined above. The objective of the union is to choose a wage rate so as to maximize the present discounted value of the infinite stream of future utility.

The One-Shot (Nash) Non-Cooperative Game

This is a simultaneous move game where the union is committed to a strategy of picking the best point on the firm's labor demand curve. The union and the firm simultaneously choose [w.sub.t] and [L.sub.t], respectively, to solve:

[Mathematical Expression Omitted].

The first order necessary conditions yield the one-shot equilibrium wage [w.sup.*], employment [L.sup.*] = [L.sup.*] ([w.sup.*]), utility [U.sup.*] = U([w.sup.*], [L.sup.*]) and profit [[Pi].sup.*] = [Pi]([w.sup.*], [L.sup.*]). This simultaneous game one-shot equilibrium (represented as point N in Figure 1) is in the nature of a Nash equilibrium and is determined at the tangency of the union indifference curve and the firm's labor demand curve.(3)

The Cooperative Game

As the one-shot game is repeated the loss from non-cooperation becomes large, which may provide incentives for the two parties to cooperate. The union may trust the firm to increase employment beyond the labor demand curve; and the firm may trust the union to accept lower wages than the one-shot Nash level of wages. Therefore with repeated interaction, both parties may do better (higher utility and higher profits) than the one-shot Nash equilibrium. The cooperative solution on the other hand, may not always be sustainable because there are one-period gains from deviation for both parties. Following the literature [3, 565-88; 7, 390-407], we assume that the non defecting parties punish the defectors through a reversion to the one-shot Nash equilibrium.(4)

For simplicity we focus attention on the set of stationary paths ([w.sub.t], [L.sub.t]) = (w, L) for all t, that Pareto-dominates the one-shot Nash equilibrium, i.e., U(w, L) [greater than] [U.sup.*] and [Pi](w, L) [greater than] [[Pi].sup.*]. Given the assumptions of this model it is straightforward to show that, for any (w, L) in this set, w [less than] [w.sup.*] and L [greater than] [L.sup.*]. A stationary path (w, L) is said to be sustainable in an equilibrium of the repeated game if it satisfies the following two conditions:

[Mathematical Expression Omitted],

[Mathematical Expression Omitted],

where, [Delta] is the common discount factor faced by both the union and the firm, [L.sup.*](w) is the employment on the labor demand curve for a given w, and [Mathematical Expression Omitted] is the wage on the zero iso-profit curve for a given L.(5) Notice that a high value of [Delta] is associated with low discounting of the future. When [Delta] [right arrow] 0, the present is all important and when [Delta] [right arrow] 1, the future is as important as the present.

Let us consider equation (6). Starting from any sustainable cooperative equilibrium, (w, L), the left hand side of equation (6) gives the one-period gain from deviation for the union. The union deviates by choosing a surprise high wage, given that firms are stuck with L for at least one period of time. It is assumed that the highest wage the union can hope to negotiate is [Mathematical Expression Omitted], such that, the firm earns zero profit, i.e., [Mathematical Expression Omitted]. A sufficient condition for this one-period gain to be positive is that the one-shot Nash level of profit is positive.(6) Figure 1 gives a graphical representation of the union's utility from deviation, starting from a sustainable equilibrium, E. The right hand side of equation (6) gives the present discounted value of the future loss to the union from deviation, the punishments starting one-period following the deviation. Hence, for the set of (w, L) satisfying equation (6), the loss from deviation exceeds the gain from deviation for the union. Hence if condition (6) holds, it does not pay the union to deviate.(7) Similarly, the left hand side of equation (7) describes the one-period gain from deviation for the firm. The firm deviates by reverting to its labor demand curve, given that the union is stuck with w, for at least one period of time. This gain is positive because [Pi](w, [L.sup.*](w)) is the envelope function of the firm's maximization problem. Once again, Figure 1 provides a graphical representation of the firm's profit from deviation, starting from point E. The right hand side of equation (7) describes the present discounted value of the future loss to the firm from deviation. Hence, for the set of (w, L) that satisfies equation (7), it does not pay the firm to deviate.

Equations (6) and (7) define the "core" or the sustainable set of (w, L), given [Delta]. The shaded area in Figure 1 represents the core for [Delta] [right arrow] 1. Of the multiple sustainable combinations we now describe the process by which the union and the firm choose the fully efficient cooperative equilibrium. Following the literature we assume that the union and the firm simultaneously choose w and L to maximize the following Nash bargain:

[Mathematical Expression Omitted],

subject to constraints (6) and (7) above, where the parameters [Rho] and (1 - [Rho]) represent the bargaining powers of the firm and the union, respectively.

If [Delta] is large enough such that neither equation (6) nor (7) is binding, then the problem reduces to a simple unconstrained maximization of J(w, L). This yields ([w.sub.c], [L.sub.c]) as the fully efficient cooperative equilibrium (point E in Figure 1); [U.sub.c] = U([w.sub.c], [L.sub.c]) is the utility at E; [[Pi].sub.c] = [Pi]([w.sub.c], [L.sub.c]) is the profit at E.

Characterization of the Solution

The propositions below characterize the solution to the above problem.

PROPOSITION I. If [Delta] [greater or equal to] max [Mathematical Expression Omitted], then the fully efficient cooperative equilibrium is always sustainable in an equilibrium of the repeated game, where [Mathematical Expression Omitted] and [Mathematical Expression Omitted], respectively, are such that,

[Mathematical Expression Omitted],

and

[Mathematical Expression Omitted].

Comment. Notice that [Delta], [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are distinct entities. [Mathematical Expression Omitted] is the lowest value of the discount factor, [Delta], that sustains the fully cooperative equilibrium ([w.sub.c], [L.sub.c]), from the union's side; [Mathematical Expression Omitted] is similarly defined for the firm. When [Delta] [greater than or equal to] max [Mathematical Expression Omitted], then neither constraint (6) nor (7) is binding, and hence ([w.sub.c], [L.sub.c]) obtains in equilibrium. Also note that the higher the value of [Mathematical Expression Omitted], the greater is the possibility that even a relatively far sighted union (with a high value of [Delta]) will find it worthwhile to deviate. This is because full cooperation will be sustained from the union's side only as long as [Mathematical Expression Omitted]. Therefore if unions have a greater inherent tendency to deviate than the firm (i.e., if [Mathematical Expression Omitted] [greater than] [Mathematical Expression Omitted]), then, ignoring the possibility of deviation by unions would lead to overestimating the possibility of full cooperation.

PROPOSITION II. There exists some [Delta] = [[Delta].sup.*], [[Delta].sup.*] [greater than] 0, such that for all [Delta] [element of] [0, [[Delta].sup.*]), no cooperation is feasible, and the one-shot Nash obtains in equilibrium.

Comment. When [Delta] [right arrow] 1, U(w, L) = [U.sup.*] and [Pi](w, L) = [[Pi].sup.*] define the frontiers of the core. Point N is the one-shot Nash equilibrium [ILLUSTRATION FOR FIGURE 2 OMITTED]. It can be shown that as [Delta] falls below 1, the union's frontier shifts to the right, excluding point N from the core, while the firm's frontier pivots around N, so as to always include it. This implies that the one-shot Nash is not a feasible equilibrium of the repeated game from the union's side, while it is always an equilibrium possibility from the firm's side.(8) As [Delta] falls, the core becomes smaller and for some [Delta] = [[Delta].sup.*], the core shrinks to a point - the point of tangency between the two frontiers. Therefore for [Delta] [element of] [0, [[Delta].sup.*]), no cooperation is viable and the two parties revert to the one-shot Nash. Figure 2 is self explanatory and gives a graphical representation of the above explanation.

The intuition behind our result is contained in equations (6) and (7). Note that the firm's Nash reaction function is the labor demand curve passing through N, while the union's Nash reaction function is the zero iso-profit locus passing above point N [ILLUSTRATION FOR FIGURE 1 OMITTED]. Consider equation (6) and let ([w.sup.*], [L.sup.*]) be a candidate for a sustainable equilibrium. It is clear that for (w, L) = ([w.sup.*], [L.sup.*]), constraint (6) can never be satisfied. The right hand side is zero while the left hand side is positive because, at [L.sup.*], it pays the union to deviate and announce a wage [Mathematical Expression Omitted]. Therefore N is not sustainable in an equilibrium of the repeated game, from the union's side. Carrying out the same exercise with equation (7), it is easy to see that, N is always an equilibrium possibility from the firm's side. Notice that the one-shot Nash would always remain an equilibrium possibility of the repeated game if we assumed that unions deviate by pushing firms to their one-shot Nash level of profits. In that case the union's Nash reaction function would pass through N. Given the arbitrariness of the latter assumption, we choose to impose the zero profit restriction, which is more reasonable from an economic point of view.

PROPOSITION III. (a). If [Mathematical Expression Omitted] when [Mathematical Expression Omitted], or, [Mathematical Expression Omitted] when [Mathematical Expression Omitted], then for [Delta] sufficiently close to the max [Mathematical Expression Omitted], an intermediate equilibrium, better than the one-shot Nash but worse than the fully efficient cooperative solution is sustainable in an equilibrium of the repeated game.

(b). If [Delta] [less than or equal to] min [Mathematical Expression Omitted], then for [Delta], [Mathematical Expression Omitted] and [Mathematical Expression Omitted] sufficiently close to each other, an intermediate equilibrium better than the one-shot Nash but worse than the fully efficient cooperative solution is sustainable in an equilibrium of the repeated game.

Comment. (a). Suppose that [Mathematical Expression Omitted]. Since [Mathematical Expression Omitted], equation (7) is satisfied for (w, L) = ([w.sub.c], [L.sub.c]), and full cooperation is sustainable by the firm. However, as [Mathematical Expression Omitted], equation (6) is violated for (w, L) = ([w.sub.c], [L.sub.c]). Hence, the union finds it worthwhile to unilaterally deviate from full cooperation. Notice that the union and the firm are assumed to be equally far sighted (as [Delta] is identical for both). Also recall (from Proposition I) that, full cooperation is sustainable by the union if [Mathematical Expression Omitted]. Hence when [Mathematical Expression Omitted] and [Mathematical Expression Omitted] is high, it implies that even a relatively far sighted union (with a high [Delta]) will find it worthwhile to deviate from full cooperation. In this sense, when [Mathematical Expression Omitted], the union has a greater inherent tendency to deviate than the firm. Since the firm gains from cooperation, it will try to "bribe" the union to cooperate. This may be done by increasing either wage or employment. Starting from point E in Figure 1, a wage hike increases the union's cooperative utility (a move to a higher indifference curve than the one that passes through point E). Recall that the union's utility from deviation is only a function of employment. Hence a wage hike does not affect the utility from deviation. Therefore, a wage hike, all else remaining constant, unambiguously increases the sustainability of cooperation for the union. On the other hand, an increase in employment, in general, has an ambiguous effect. A higher employment, [L.sub.A] [greater than] [L.sub.c], will increase the union's cooperative utility (a move to a higher indifference curve than at E). But [L.sub.A] is associated with a new surprise wage [Mathematical Expression Omitted]. When [Mathematical Expression Omitted] falls between points X and Y in Figure 1, the union's utility from deviation rises higher than [Mathematical Expression Omitted]. Hence the final effect of an employment increase is ambiguous.(9) This process of bribing gets the union and the firm to move away from the fully efficient cooperative equilibrium, which is not sustainable any more. The two parties then settle at an equilibrium which lies somewhere in between the one-shot Nash and the fully efficient cooperative equilibrium, as long as [Mathematical Expression Omitted]. For [Mathematical Expression Omitted], cooperation breaks down completely.

The case where [Mathematical Expression Omitted] works symmetrically. The union "bribes" the firm to cooperate. Such bribing increases the payoff from cooperation to the firm, thereby reducing their incentive to deviate. Unions suffer lower payoffs but still do better than the one-shot Nash. It can be shown that when the firm deviates, allowing them to lay off workers is an unambiguous way of increasing their net benefit from cooperation. Wage reductions increase the profits from cooperation but may also increase the profit from deviation. Hence the net effect may go either way.

(b). Since [Delta] is less than both [Mathematical Expression Omitted] and [Mathematical Expression Omitted], it pays both parties to deviate from cooperation. It is intuitive that it is harder to sustain cooperation in this case than when [Delta] lies in between the two critical values. But for [Delta], [Mathematical Expression Omitted] and [Mathematical Expression Omitted] sufficiently close, some intermediate cooperation may be sustainable. If the gap between [Mathematical Expression Omitted] and [Mathematical Expression Omitted] is very large, then one of the parties (the one with the higher critical delta) has to be bribed by a very large amount to cooperate. This can soon become extremely costly for the other party who can then make more by not cooperating. Hence cooperation breaks down.

In summary, the above propositions show that when both parties have the power to deviate, sustainability of some cooperation is not guaranteed. In fact the one-shot Nash monopoly union equilibrium obtains over a large range of the discount factor, [Delta] [element of] [0, [[Delta].sup.*]). This striking result is in sharp contrast to the Espinosa and Rhee [3] result where, for all [Delta] [greater than] 0, some cooperation is always sustainable and the one-shot Nash obtains in an equilibrium of the repeated game only when [Delta] = 0. Also, when the union has a greater inherent tendency to deviate (i.e., [Mathematical Expression Omitted]) and does so by asking for a surprise wage increase, the firm may prefer bribing the union by raising wages. This will most likely be the case when an increase in employment has an ambiguous impact on raising the sustainability of cooperation for the union because it increases the utility from deviation for the union (Proposition III(a)). In that case we expect the union to enjoy a steeper wage-employment path as compared to the case where the union cannot deviate.(10) The following example helps to clarify the intuition behind the analytical propositions discussed above.

III. An Example

We specify a modified Stone Geary utility function for the union as:

U(w, L) = 0.5[(w - [w.sub.a]).sup.[Theta]]L, (11)

where [w.sub.a] is the relevant alternative wage and [Theta] is the relative weight that unions place on wages versus employment. The inverse demand function is P(Q) = b - Q; the production function is Q = F(L) = [L.sup.[Alpha]], (0 [less than] [Alpha] [less than] 1). We choose [Theta] = 0.8, [w.sub.a] = 1, [Alpha] = 0.75, b = 10 and [Rho] = 0.5. We get the following equilibria for both the Espinosa and Rhee (E&R) and the Simultaneous Game (SG) models:

One-shot Nash equilibrium: [w.sup.*] = 3.17 [L.sup.*] = 2.92 [U.sup.*] = 2.72 [[Pi].sup.*] = 8.08.

Fully efficient cooperative equilibrium: [w.sub.c] = 2.07 [L.sub.c] = 6.8 [U.sub.c] = 3.6 [[Pi].sub.c] = 10.3.

The differences in the two models arise out of the different assumptions made about the nature of deviation of unions. In the SG model, the union deviates by a surprise wage demand. Equation (6) gives the union's sustainability condition after substituting the above functional forms. Recall (footnote 7) that the sustainability condition for the union in the E&R model is given by: [U(w, L) - [U.sup.*]] [greater than or equal to] 0. Firms behave identically in the two models and their sustainability condition is given by equation (7) after substituting the assumed functional forms. We find that [Mathematical Expression Omitted], [Mathematical Expression Omitted] and [[Delta].sup.*] = 0.688.

Figure 3 and Figure 4 compare the wage and employment paths, respectively, for the two models, as [Delta] falls from 1 to 0. The two graphs show that for a given [Delta], wage is higher and employment is lower when the union has the power to deviate (SG model). Figure 5 compares the wage-employment paths for the two models. Point E is the fully efficient cooperative equilibrium and N is the one-shot Nash equilibrium. Notice that the value of [Delta] falls as one moves along the graph from E to N. In the E&R model, E is sustainable for all [Delta] [element of] [0.44, 1]; some intermediate cooperation is sustainable for all [Delta] [element of] [0, 0.44]; and only N is sustainable for [Delta] = 0. In the intermediate range (i.e., when [Delta] [element of] (0, 0.44)) the union has to "bribe" the firm to cooperate. This is done by allowing the firms to reduce employment. However the union has to receive a higher utility than the one-shot Nash utility, for cooperation to be viable. Hence wages rise rapidly as [Delta] falls very low, giving rise to a negatively sloped wage employment path.

Look at the wage-employment path of the SG model [ILLUSTRATION FOR FIGURE 5 OMITTED]. Notice that [Mathematical Expression Omitted], suggesting that the union has a greater tendency of breaking cooperation. Point E is sustainable for [Delta] [element of] [0.81, 1]; an intermediate cooperative equilibrium is sustained for [Delta] [element of] [0.688, 0.81); N is the equilibrium for [Delta] [element of] [0, 0.688). Notice that as [Delta] falls below 0.81, the firm has to "bribe" the union to cooperate. This is done by granting wage hikes. However the firm has to make more profits than the one-shot Nash level of profits for cooperation to be viable. Therefore employment falls along with wage hikes. Figure 5 reflects our strong intuition that since the union can threaten the firm with deviation in the SG model, they should be able to get a better bargain from the firm - a higher wage for a given level of employment.

IV. Concluding Comments

This paper investigates the possibility of union deviation over wages in the context of a simultaneous move, repeated game model. Unlike the established results in the literature, we see that some cooperation is not guaranteed and the non-cooperative Monopoly Union equilibrium obtains over large ranges of the discount factor. A lot of attention has been paid to the extraordinary increase in wages during the late 1970s in industries with slow and declining growth rates. The existing literature recognizes the fact that a wage hike is quite likely when both parties expect the game to end in the near future (interpreted as [Delta] [right arrow] 0 for both the union and the firm). This paper shows that the wage-employment path may be steeper when both parties have the power to deviate than when the firm alone can deviate. Therefore, ignoring the possibility of union deviation may underestimate the extent of the wage hike for a given level of employment. Finally, substantial empirical work alone can settle the question regarding the empirical relevance of the different models. This should be a fruitful area for future research.

This paper is from a chapter of my Ph.D. dissertation at the University of Maryland. I thank John Haltiwanger, Katherine Abraham, Edward Montgomery, Robert Schwab and seminar participants at the University of Maryland for helpful comments on earlier drafts of this paper. I am also grateful to an anonymous referee for helpful comments and suggestions. Any remaining errors are mine.

1. The Monopoly Union model owes its origins to Dunlop [2]. The Efficient Contract model was analyzed by Leontief [4, 76-79]. For an overall perspective of this literature see Oswald [5, 160-93].

2. Note that "deviation" has a particular meaning in the context of this paper. Based on a history of successful long term relationship each party expects the other to choose the cooperative configurations. Hence the firm "deviates" by choosing a lower employment than what the union expects. The union "deviates" by announcing a high wage so as to surprise the firm. Bandyopadhyay [1] considers union deviation by reducing effort to increase wages per efficiency units of labor.

3. Notice that this simultaneous game one-shot equilibrium is identical to the familiar Monopoly Union equilibrium which is defined in a sequential setting with the union behaving as the leader. With the commitment on the part of the union, in a simultaneous setting, the firm does not have to wait in real time to pick the leadership level of employment, [L.sup.*]. Rasmusen [6, 76-105] describes a similar equilibrium in the context of oligopoly in the product market.

4. For simplicity we have precluded renegotiation at the beginning of the punishment period.

5. In general, [Delta] may be different for the union and the firm. They have been assumed to be equal in this model, for analytical simplicity.

6. Assuming that V(0) = F(0) = 0, V[prime](0) [not equal to] 0, F[prime] (0) [not equal to] 0, V[double prime] (0) [less than or equal to] 0 and F[double prime] (0) [not equal to] 0, the one-shot Nash profits can be shown to be positive.

7. Notice that in the Espinosa and Rhee [3] model, the union's sustainability condition is [U(w, L) - U([w.sup.*], [L.sup.*]) [greater than or equal to] 0], which is derived from equation (6) above by letting [Delta] [right arrow] 1. In such a framework, unilateral deviation is never an option for the union, and the sustainability of cooperation is determined entirely by the firm.

8. Algebraically, this result is obtained by calculating [Delta]w/[Delta][Delta] for the union from equation (6) and [Delta]L/[Delta][Delta] for the firm from equation (7), assuming [Delta] [not equal to] 1. It works out that [Delta]w/[Delta][Delta] [less than] 0 (for the union) while [Delta]L/[Delta][Delta] [greater than] 0 (for the firm). When evaluated at N, [Delta]L/[Delta][Delta] = 0, while [Delta]w/[Delta][Delta] [less than] 0.

9. Note that if the absolute value of the slope of the indifference curve is lower than that of the zero iso-profit curve at point X in Figure 1, then an increase in employment will unambiguously increase the sustainability of cooperation from the union's side.

10. Note that this is a possibility only. In general, the analytical possibilities are many and finally depend on the underlying functional forms and parameter values.

References

1. Bandyopadhyay, Sudeshna C. "Endogenous Effort in a Dynamic Model of Union-Firm Interaction." Working Paper, University of Maryland, 1993.

2. Dunlop, John T. Wage Determination Under Trade Unions. New York: Macmillan, 1944.

3. Espinosa, Maria P. and Changyong Rhee, "Efficient Wage Bargaining as a Repeated Game." Quarterly Journal Of Economics, August 1989, 565-88.

4. Leontief, Wassily, "The Pure Theory of the Guaranteed Annual Wage Contract." Journal of Political Economy, February 1946, 76-79.

5. Oswald, Andrew J., "The Economic Theory of Trade Unions: An Introductory Survey." Scandinavian Journal of Economics, 87 (2), 1985, 160-93.

6. Rasmusen, Eric. Games and Information: An Introduction to Game Theory. Basil Blackwell, 1989, 76-105.

7. Rotemberg, Julio and Garth Saloner, "A Supergame-Theoretic Model of Price Wars During Booms." American Economic Review, June 1986, 390-407.
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Author:Bandyopadhyay, Sudeshna C.
Publication:Southern Economic Journal
Date:Oct 1, 1995
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