Discounted and Finitely Repeated Minority Games with Public Signals

Posted: 12 Mar 2012

See all articles by Jerome Renault

Jerome Renault

University of Toulouse 1 - Toulouse School of Economics (TSE)

Marco Scarsini

Luiss University Dipartimento di Economia e Finanza

sergio scarlatti

affiliation not provided to SSRN

Date Written: March, 10 2012

Abstract

We consider a repeated game where at each stage players simultaneously choose one of the two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. [Renault, J., Scarlatti, S., Scarsini, M., 2005. A folk theorem for minority games. Games Econom. Behav. 53 (2), 208–230], who proved a folk theorem. Here we consider a discounted version and a finitely repeated version of the game, and we strengthen our previous result by showing that the set of equilibrium payoffs Hausdorff-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to infinity. We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria.

Keywords: Repeated games, Imperfect monitoring, Public equilibria, Private equilibria, Pareto-efficiency, Discount factor

JEL Classification: C72

Suggested Citation

Renault, Jerome and Scarsini, Marco and scarlatti, sergio, Discounted and Finitely Repeated Minority Games with Public Signals (March, 10 2012). Mathematical Social Sciences, Vol. 56, No. 1, 2008, Available at SSRN: https://ssrn.com/abstract=2019688

Jerome Renault

University of Toulouse 1 - Toulouse School of Economics (TSE) ( email )

Place Anatole-France
Toulouse Cedex, F-31042
France

Marco Scarsini (Contact Author)

Luiss University Dipartimento di Economia e Finanza ( email )

Viale Romania 32
Rome, RM 00197
Italy

Sergio Scarlatti

affiliation not provided to SSRN

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