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Coalition-Stable Equilibria in Repeated Games

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Author Info
Anthony Fai-Tong Chung

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Abstract

It is well-known that subgame-perfect Nash equilibrium does not eliminate incentives for joint-deviations or renegotiations. This paper presents a systematic framework for studying non-cooperative games with group incentives, and offers a notion of equilibrium that refines the Nash theory in a natural way and answers to most questions raised in the renegotiation-proof and coalition-proof literature. Intuitively, I require that an equilibrium should not prescribe in any subgame a course of action that some coalition of players would jointly wish to deviate, given the restriction that every deviation must itself be self-enforcing and hence invulnerable to further self-enforcing deviations. The main result of this paper is that much of the strategic complexity introduced by joint-deviations and renegotiations is redundant, and in infinitely-repeated games with discounting every equilibrium outcome can be supported by a stationary set of optimal penal codes as in Abreu (1988). In addition, I prove existence of equilibrium both in stage games and in repeated games, and provide an iterative procedure for computing the unique equilibrium-payoff set

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Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 581.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:581

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Related research
Keywords: Coalition; Renegotiation; Game Theory;

Find related papers by JEL classification:
C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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  1. DeMarzo, Peter M., 1992. "Coalitions, leadership, and social norms: The power of suggestion in games," Games and Economic Behavior, Elsevier, vol. 4(1), pages 72-100, January. [Downloadable!] (restricted)
  2. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March. [Downloadable!] (restricted)
  3. Ray Debraj, 1994. "Internally Renegotiation-Proof Equilibrium Sets: Limit Behavior with Low Discounting," Games and Economic Behavior, Elsevier, vol. 6(1), pages 162-177, January. [Downloadable!] (restricted)
  4. Greenberg, Joseph, 1989. "Deriving strong and coalition-proof nash equilibria from an abstract system," Journal of Economic Theory, Elsevier, vol. 49(1), pages 195-202, October. [Downloadable!] (restricted)
  5. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July. [Downloadable!] (restricted)
  6. Bergin James & MacLeod W. Bentley, 1993. "Efficiency and Renegotiation in Repeated Games," Journal of Economic Theory, Elsevier, vol. 61(1), pages 42-73, October. [Downloadable!] (restricted)
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  7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  8. Milgrom, Paul & Roberts, John, 1996. "Coalition-Proofness and Correlation with Arbitrary Communication Possibilities," Games and Economic Behavior, Elsevier, vol. 17(1), pages 113-128, November. [Downloadable!] (restricted)
  9. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December. [Downloadable!] (restricted)
  10. Osborne, Martin J., 1990. "Signaling, forward induction, and stability in finitely repeated games," Journal of Economic Theory, Elsevier, vol. 50(1), pages 22-36, February. [Downloadable!] (restricted)
  11. Asheim, G.B., 1988. "Extending Renegotiation-Proofness To Infinite Horizon Games," Papers 16-88, Norwegian School of Economics and Business Administration-.
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  12. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-28, May. [Downloadable!] (restricted)
  13. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May. [Downloadable!] (restricted)
  14. Farrell Joseph, 1993. "Meaning and Credibility in Cheap-Talk Games," Games and Economic Behavior, Elsevier, vol. 5(4), pages 514-531, October. [Downloadable!] (restricted)
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