Abstract

By large games, we mean ones in which the number of players is so large that players do not even know how many players are in the game, let alone about how everyone plays. Payoffs are then determined by strategy distributions rather than profiles, and heuristics like imitation become interesting. We consider a neighbourhood structure on these games in which players play normal form games within neighbourhoods but switch neighbourhoods based on observations. We then study the eventual stability of configurations in this context for finite memory player types.

In such games it is also interesting to study the ‘social cost’ of providing options to players. We consider an implicit player – the society, who makes actions available to players and incurs certain costs in doing so. But then when few players play a strategy it may become infeasible to support it and hence society may remove it altogether, leading to a new situation. Once again we discuss questions of eventual stability and synthesis of rules for society (when to intervene and how).

The work reported is joint with Soumya Paul (Toulouse) and Sunil Simon (Amsterdam).