Abstract: How would you strategize in a game with say, 50 players? If the game were repeated many times, and you saw that your neighbour was doing well in several previous rounds, would you be tempted to imitate the neighbour in the next round ? Would that be rational on your part ?
In games with a large number of players, outcomes are associated not with the actual tuple of strategies chosen by players but with the distribution of what fraction of players choose which move. The pattern of reasoning in such games is different from those in which all players know each others' types. We discuss Nash equilibria, and some logical / automata theoretic formulations of stability in such games.