Limited Foresight Equilibrium

This paper models a scenario where finite perfect-information games are distorted in two ways. First, each player can have different possible levels of foresight, where foresight is a particular number of future stages that the player can observe/understand from each of her moves. In particular, each player's foresight is allowed to be “limited” or insufficient to observe the entire game from each move. Second, there is uncertainty about each opponent's foresight. I define the Limited Foresight Equilibrium (LFE) for this model. An LFE specifies how limited-foresight players' strategies and beliefs about opponents' foresight evolve as they move through the stages of the game. I show the existence of LFE and describe its other properties. I show that in LFE limited-foresight players follow simple heuristics for beliefs and actions. As applications, LFE is shown to rationalize experimental findings on Sequential Bargaining and the Centipede game.