Dynamics Of Choice Restriction In Large Games

We study games in which the number of players are large, and hence outcomes are independent of the identities of the players. Game models typically study how choices made by individual rational players determine game outcomes. We extend this model to include an implicit player — the society, who makes actions available to players and incurs certain costs in doing so. In the course of play, an optionamay be chosen only by a small number of players and hence may become too expensive to maintain, so the society may remove it from the set of available actions. This results in a change in the game and the players strategize afresh taking this change into account. We highlight the mutual recursiveness of individual rationality and societal rationality in this context. Specifically, we study two questions: When players play according to given strategy specifications, which actions of players should the society restrict and when, so that the social cost is minimized eventually? Conversely, assuming a set of rules by which society restricts choices, can players strategize in such a way as to ensure certain outcomes? We discuss solutions in finite memory strategies.