A folk theorem for minority games

We study a particular case of repeated games with public signals. In the stage game an odd number of players have to choose simultaneously one of two rooms. The players who choose the less crowded room receive a reward of one euro (whence the name “minority game”). The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payoff can be achieved as a uniform equilibrium payoff, and as an almost sure equilibrium payoff. In particular we construct an inefficient equilibrium where, with probability one, all players choose the same room at almost all stages. This equilibrium is sustained by punishment phases which use, in an unusual way, the pure actions that were played before the start of the punishment.

[1]  Steven Haberman,et al.  Optimal investment strategies and risk measures in defined contribution pension schemes , 2002 .

[2]  L. Montrucchio,et al.  Cores and stable sets of finite dimensional games , 2003 .

[3]  W. Arthur.  Inductive Reasoning and Bounded Rationality , 1994 .

[4]  Massimo Marinacci,et al.  Probabilistic Sophistication and Multiple Priors , 2002 .

[5]  Ehud Lehrer,et al.  On the equilibrium payoffs set of two player repeated games with imperfect monitoring , 1992 .

[6]  Claudio Mattalia,et al.  APPLIED MATHEMATICS WORKING PAPER SERIESExistence of Solutions and Asset Pricing Bubbles in General Equilibrium Models , 2002 .

[7]  Ehud Lehrer,et al.  Two-Player Repeated Games with Nonobservable Actions and Observable Payoffs , 1992, Math. Oper. Res..

[8]  Fabio Privileggi,et al.  Wealth Polarization and Pulverization in Fractal Societies , 2002 .

[9]  Drew Fudenberg,et al.  The Folk Theorem in Repeated Games with Discounting or with Incomplete Information , 1986 .

[10]  Jonathan P. Thomas,et al.  The Folk Theorem in Repeated Games ofIncomplete , 1997 .

[11]  Domenico Menicucci,et al.  APPLIED MATHEMATICS WORKING PAPER SERIESOptimal Two-Object Auctions with Synergies * , 2001 .

[12]  S. Hart,et al.  Handbook of game theory with economic applications: volume 3 , 1993 .

[13]  W. Arthur,et al.  Complexity and the economy , 2014, Science.

[14]  David Pearce,et al.  Information and timing in repeated partnerships , 1991 .

[15]  William H. Ruckle,et al.  BV as a Dual Space. , 2001 .

[16]  Massimo Marinacci,et al.  Ambiguity from the Differential Viewpoint , 2002 .

[17]  Marco Scarsini,et al.  The convexity-cone approach to comparative risk and downside risk , 2003 .

[18]  Andrea Roncoroni.  Change of numéraire for affine arbitrage pricing models driven by multifactor marked point processes , 2001 .

[19]  Tristan Tomala,et al.  Communication equilibrium payoffs in repeated games with imperfect monitoring , 2004, Games Econ. Behav..

[20]  Andrea Cavagna,et al.  THERMAL MODEL FOR ADAPTIVE COMPETITION IN A MARKET , 1999 .

[21]  Massimo Marinacci,et al.  APPLIED MATHEMATICS WORKING PAPER SERIESInsurance Premia Consistent with the Market ∗ , 2002 .

[22]  Jérôme Renault,et al.  On Two-Player Repeated Games with Lack of Information on One Side and State-Independent Signalling , 2000, Math. Oper. Res..

[23]  Tristan Tomala,et al.  Nash Equilibria of Repeated Games with Observable Payoff Vectors , 1999 .

[24]  Fabio Maccheroni,et al.  Expected utility theory without the completeness axiom , 2004, J. Econ. Theory.

[25]  Rick L. Riolo,et al.  Adaptive Competition, Market Efficiency, and Phase Transitions , 1999 .

[26]  S. Sorin.  Chapter 4 Repeated games with complete information , 1992 .

[27]  L. Montrucchio,et al.  Subcalculus for set functions and cores of TU games , 2003 .

[28]  Massimo Marinacci,et al.  Certainty Independence and the Separation of Utility and Beliefs , 2005, J. Econ. Theory.

[29]  Massimo Marinacci,et al.  APPLIED MATHEMATICS WORKING PAPER SERIESHOW TO CUT A PIZZA FAIRLY: , 2002 .

[30]  Massimo Marinacci,et al.  Random Correspondences as Bundles of Random Variables , 2001 .

[31]  E. Lehrer.  Lower equilibrium payoffs in two-player repeated games with non-observable actions , 1989 .

[32]  Massimo Marinacci,et al.  A Subjective Spin on Roulette Wheels , 2001 .

[33]  Umberto Cherubini,et al.  Pricing Vulnerable Options with Copulas , 2001 .

[34]  Ehud Lehrer,et al.  Nash equilibria of n-player repeated games with semi-standard information , 1990 .

[35]  Massimo Morelli,et al.  Credit Rationing, Wealth Inequality, and Allocation of Talent , 2002 .

[36]  F. Maccheroni,et al.  Coherence without additivity , 2003 .

[37]  Yi-Cheng Zhang,et al.  Emergence of cooperation and organization in an evolutionary game , 1997 .

[38]  Luigi Montrucchio,et al.  APPLIED MATHEMATICS WORKING PAPER SERIESOn Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type ∗ , 2001 .

[39]  Tristam Tomala.  Pure equilibria of repeated games with public observation , 1998 .

[40]  Physics Department,et al.  Adaptive Competition, Market Efficiency, Phase Transitions and Spin-Glasses , 1997 .

[41]  Fabio Maccheroni,et al.  APPLIED MATHEMATICS WORKING PAPER SERIESYaari dual theory without the completeness axiom ∗ , 2001 .

[42]  Massimo Marinacci,et al.  A characterization of the core of convex games through Gateaux derivatives , 2004, J. Econ. Theory.

[43]  Umberto Cherubini,et al.  Multivariate Option Pricing with Copulas , 2000 .

[44]  Sylvain Sorin,et al.  On Repeated Games with Complete Information , 1986, Math. Oper. Res..

[45]  Tristan Tomala,et al.  Pure equilibria of repeated games with public observation , 1998, Int. J. Game Theory.