Observable Strategies

The idea that reciprocal cooperation can be obtained in a one-shot game if the players observe each other’s strategies before taking action has attracted many authors. From a strictly logical perspective, however, there cannot be such games. Nevertheless, there are games in which each player can observe which class, out of a collection of classes smaller than the number of strategies, the opponent’s strategy belongs to. For any underlying 2-player, finite, normal-form game there is a game extendedwith such coarsely observable strategies that has equilibria with payoffs arbitrarily close to any feasible, individually rational payoff profile.