Observable Strategies, Commitments, and Contracts

We consider rules (strategies, commitments, contracts, or computer programs) that make behavior contingent on an opponent's rule. The set of perfectly observable rules is not well defined. Previous contributions avoid this problem by restricting the rules deemed admissible. We instead limit the information available about rules. Each player can only observe which class, out of a collection of classes smaller than the number of rules, the opponent's rule belongs to. For any underlying 2-player, finite, normal-form game there is a game extended with coarsely observable strategies that has equilibria with payoffs arbitrarily close to any feasible, individually rational payoff profile.