Abstract

In large anonymous games, payoffs are determined by strategy distributions rather than strategy profiles. If half the players choose a strategy a, all of them get a certain payoff, whereas if only one-third of the players choose that strategy, the players choosing may get a different payoff. Strategizing in such a game by a player involves reasoning about not who does what but what fraction of the population makes the same choice as that player.We present a simple modal logic to reason about such strategization in large games. Since actual numbers are irrelevant, a player need not even know how many others are in the game, thus leading to the consideration of games with unboundedly many players. The logic we consider is the propositional modal fragment of a first order modal logic. We show that it has a bounded agent property, giving us a decision procedure for satisfiability. We also present a complete axiomatization of the valid formulas. The logic admits a natural model checking algorithm and bisimulation characterization. The logic with quantification over players is more appropriate, but is undecidable.