Some First Results for Noncooperative Pregames: Social Conformity and Equilibrium in Pure Strategies

We introduce the framework of noncooperative pregames and demonstrate that for all games with sufficiently many players, there exist approximate (ε) Nash equilibria in pure strategies. In fact, every mixed strategy equilibrium can be used to construct an ε-equilibrium in pure strategies — ours is an ‘ε-purification’ result. Our main result is that there exists an ε- equilibrium in pure strategies with the property that most players choose the same strategies as all other players with similar attributes. More precisely, there is an integer L, depending on ε but not on the number of players, so that any sufficiently large society can be partitioned into fewer than L groups, or cultures, consisting of similar players, and all players in the same group play the same pure strategy. In ongoing research, we are extending the model to cover a broader class of situations, including incomplete information. We would be grateful for any comments that might help us improve the paper