Abstract
This book analyzes countable infinite repetition of interaction between firms on both sides of a market, with discounting of future profits.1 Our first aim is to prove the sufficient conditions for the existence of equilibria, which take into account the deviations by the coalitions, in it. We explain the reasons for our choice of solution concepts in Sect. 1.1 of Chap. 1.
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- 1.
Throughout the book we use the well-established term “repeated game” for what [Mertens (1989)] refers to as the “supergame.”
- 2.
Throughout the book, we use the term “analyzed market” for the market modeled by the stage game (of the repeated game that is the object of our study). Besides this market, the firms’ payoffs are influenced by the market in which the buyers in the analyzed market earn their revenue. The latter market is either a retail market for the goods traded in the analyzed market or, if buyers are themselves producers, a market for their products.
- 3.
Throughout the book, the term “price” always implies the unit price.
- 4.
This is certainly not unrealistic. Moreover, traded quantities and prices cannot be given by a supply function or a demand function in the analyzed market. These functions are derived under the assumption of price taking behavior on one side of the market. Such assumption would limit the possibilities for cooperation in the repeated game.
- 5.
If there was at least one producer trading with all buyers along the equilibrium path and the stage game payoff functions were continuous, the grand coalition can also strictly Pareto improve the vector of payoffs in the repeated game. The method of doing so would be analogous to the one in Step 4 in Sect. 4.3.2.
- 6.
A continuation equilibrium in a subgame is a restriction of an equilibrium strategy profile to that subgame. The continuation equilibrium payoff vector is the payoff vector generated by the continuation equilibrium.
- 7.
[Bernheim et al. (1987)] study only finite horizon games. Various concepts of renegotiation-proofness for infinite horizon discrete time games with two players (mentioned below in the text) impose restrictions on the strategy profiles to which the grand coalition can deviate, or, in the case of [Maskin & Tirole (1988)], restrict attention to Markov strategies.
- 8.
Despite the title of the paper a strong Nash equilibrium is a solution concept for noncooperative games. See also [Bernheim et al. (1987), p.2-3].
- 9.
Both benchmarks are non-spatial. Nevertheless, this does not reduce the value of our results because the comparison of various forms of competitive behavior with collusion is more favorable for the former in a non-spatial setting.
- 10.
In the case of imperfect competition on both sides of a market, we would need a non-collusive model of bargaining in order to determine the prices and quantities. There is no generally known model of this type. Therefore, we prefer to work with a monopsony model and a Cournot oligopoly.
References
Aumann, R.J. “Acceptable Points in General Cooperative n-person Games,” Annals of Mathematical Studies Series 40 (1959), 287-324.
Bernheim, B.D., B. Peleg, and M.D. Whinston: “Coalition-Proof Nash equilibria I. Concepts,” Journal of Economic Theory 42 (1987), 1-12.
Bernheim, B.D. and D. Ray: “Collective Dynamic Consistency in Repeated Games,” Games and Economic Behavior 1 (1989), 295-326.
Chandler, A.D. Jr.: Scale and Scope. The Dynamics of Industrial Capitalism. Cambridge, MA: The Belknap Press of the Harvard University Press, 1990.
“Commission Action Against Cartels – Questions and Answers.” MEMO 10/290, 30 June 2010. http://europa.eu/rapid/pressReleasesAction.do?reference=MEMO/10/290&format=HTML&aged=0&language=EN&guiLanguage=en
Farrell, J.: Renegotiation in Repeated Oligopoly Games. Mimeo. University of California at Berkeley, 1993.
Farrell, J. and E. Maskin: “Renegotiation in Repeated Games,” Games and Economic Behavior 1 (1989), 327-360.
Greenhut, M.L., G. Norman, and C. Hung: The Economics of Imperfect Competition. Cambridge: Cambridge University Press, 1987.
Horniaček, M.: “The Approximation of a Strong Perfect Equilibrium in a Discounted Supergame,” Journal of Mathematical Economics 25 (1996), 85-107.
Kreps, D.M. and J.A. Scheinkman: “Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes,” Bell Journal of Economics 14 (1983), 326-337.
Maskin, E. and J. Tirole: “A Theory of Dynamic Oligopoly II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles,” Econometrica 56 (1988), 571-599.
Mertens, J.-F.: “Supergames,” in The New Palgrave: Game Theory, ed. by J. Eatwell, M. Milgate, and P. Newman. New York: W.W. Norton, 1989, 238-241.
Rubinstein, A: : “Strong Perfect Equilibrium in Supergames,” International Journal of Game Theory 9 (1980), 1-12.
Selten, R.: “Spieltheoretische Behandlung eines Oligopolmodells mit Nachfrageträgheit,” Zeitschrift für die Gesamte Staatswissenschaft 121 (1965), 301-324 and 667-689.
Selten, R.: “Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games,” International Journal of Game Theory 4 (1975), 25-55.
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Horniaček, M. (2011). Introduction. In: Cooperation and Efficiency in Markets. Lecture Notes in Economics and Mathematical Systems, vol 649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19763-5_1
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