×

zbMATH — the first resource for mathematics

Renegotiation in repeated games. (English) Zbl 0754.90082
Summary: In repeated games, subgame-perfect equilibria involving threats of punishment may be implausible if punishing one player hurts the other(s). If players can renegotiate after a defection, such a punishment may not be carried out. We explore a solution concept that recognizes this fact, and show that in many games the prospect of renegotiation strictly limits the cooperative outcomes that can be sustained. We characterize those outcomes in general, and in the prisoner’s dilemma, Cournot and Bertrand duopolies, and an advertising game in particular.

MSC:
91A20 Multistage and repeated games
91B26 Auctions, bargaining, bidding and selling, and other market models
90B60 Marketing, advertising
91A80 Applications of game theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abreu, D; Pearce, D; Stacchetti, E, Renegotiation and symmetry in repeated games, (1989), Yale University, May
[2] Asheim, G, Extending renegotiation-proofness to infinite horizon games, (1989), Norwegian School of Economics and Business, mimeo, revised · Zbl 0755.90098
[3] Benoit, J.-P; Krishna, V, Renegotiation in finitely repeated games, Harvard business school working paper 89-004, (1988)
[4] Bergin, J; McLeod, W.B, Efficiency and renegotiation in repeated games, (1989), Queen’s University, mimeo
[5] Bernheim, B.D; Peleg, B; Whinston, M, Coalition-proof Nash equilibrium. I. concepts, J. econ. theory, 42, 1-12, (1987) · Zbl 0619.90090
[6] Bernheim, B.D; Ray, D, Collective dynamic consistency in repeated games, Games econ. behav., 1, 295-326, (1989) · Zbl 0754.90081
[7] Blume, A, Renegotiation-proof theories in finite and infinite games, (1987), U.C. San Diego, November
[8] Cave, J, Long-term competition in a dynamic game: the cold fish war, Rand J. econ., 18, 596-610, (1987)
[9] van Damme, E, Renegotiation-proof equilibria in repeated prisoners’ dilemma, J. econ. theory, 46, 206-217, (1989) · Zbl 0688.90065
[10] Evans, R; Maskin, E, Efficient renegotiation-proof equilibria in repeated games, Games econ. behav., 1, 361-369, (1989) · Zbl 0777.90092
[11] Farrell, J; Maskin, E, Renegotiation in repeated games, (), June · Zbl 0754.90082
[12] Fudenberg, D; Levine, D, Subgame-perfect equilibria of finite- and infinite-horizon games, J. econ. theory, 31, 251-268, (1983) · Zbl 0521.90106
[13] Fudenberg, D; Maskin, E, The folk theorem in repeated games with discounting or with incomplete information, Econometrica, 54, 533-554, (1986) · Zbl 0615.90099
[14] Fudenberg, D; Maskin, E, On the dispensability of public randomization in discounted repeated games, (1988), Harvard and MIT, mimeo · Zbl 0719.90106
[15] de Marzo, P, Coalitions and sustainable social norms in repeated games, IMSSS technical report 529, (1988), Stanford
[16] Maskin, E; Tirole, J, A theory of dynamic oligopoly, II: price competition, kinked demand curves, and Edgeworth cycles, Econometrica, 56, 571-599, (1988) · Zbl 0664.90023
[17] Maskin, E; Tirole, J, Markov equilibrium, (1989), MIT, mimeo
[18] Pearce, D, Renegotiation-proof equilibria: collective rationality and intertemporal cooperation, (1987), mimeo, Yale
[19] Rubinstein, A, Strong perfect equilibrium in supergames, Int. J. game theory, 9, 1-12, (1980) · Zbl 0433.90093
[20] Shapley, L, On the nonconvergence of fictitious play, RAND memorandum RM-3026-PR, (1962)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.