Discounted and finitely repeated minority games with public signals

Abstract

We consider a repeated game where at each stage players simultaneously choose one of 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. (2005), 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.

Perfect information games where each player acts only once

“…Minority games have been used to model a variety of different phenomena ranging from congestion, downloading in P2P networks, market entry, to speculative behavior in financial markets. For an extensive list of related works, we refer to Renault et al (2007) and Renault et al (2008).…”

General Properties of Long-Run Supergames

“…(4) A deviation may be detected by all players, yet the identity of the deviator remains unknown [37,38,46]. (5) The independent minmax v i is the punishment level of player i in case of perfect observation.…”

Finitely repeated games with semi-standard monitoring

“…This result is specific to mixed strategies, as any pure strategy is fully equivalent to a pure public strategy. Finally, Renault et al (2008) prove a Folk Theorem for finitely repeated minority games with public signals. Note that the monitoring structure of this game is not semi-standard and that specific properties of the minority games are used extensively in Renault et al (2008).…”

“…Surprisingly little attention has been paid to finitely repeated games with imperfect monitoring, notable exceptions being the works of Sekiguchi (2001), Mailath et al (2002), and Renault et al (2008). However, these results are quite specific and to the best of our knowledge, no Folk-Theorem-like result is known for a reasonably wide class of games with imperfect monitoring.…”