Discounted repeated minority games with public signals J.Renault S. Scarlatti M.Scarsini

Following a suggestion in Arthur (1994) many authors have considered a class of games called minority games, where each player repeatedly acts trying to choose the action that is less popular among all players. In many real life situations it is preferable to be in the minority. Think for instance of a residential suburban area that is linked to downtown by two main roads. Commuters have to decide every morning which road to take and, for obvious reasons, they all want to avoid traffic. Since the commuter typically do not recognize their fellow commuters on the road, but only perceive the existence of traffic, this phenomenon can be modelled as a game with imperfect public monitoring. In general this class of games is interesting when several agents must take decentralized decision on whether to access a scarce resource, knowing that at most a fixed number of them will be able to enjoy its benefits. Similar situations have been analyzed by the empirical economic literature on market entry games (see e.g., Selten and Guth (1982); Ochs (1990, 1995); Rapoport et al. (2002); Erev and Rapoport (1998)). In these models players must decide independently whether to enter a market (and incur an entry cost). Since capacity is limited, the entrants will reap a reward only if their number is smalle