What Situation Is This? Coarse Cognition and Behavior Over a Space of Games

We study strategic interaction between agents who distill the complex world around them into simpler situations. Assuming agents share the same cognitive frame, we show how the frame affects equilibrium outcomes. In one-shot and repeated interactions, the frame causes agents to be either better or worse off than if they could perceive the environment in full detail: it creates a fog of cooperation or a fog of conflict. In repeated interaction, the frame is as important as agents' patience in determining the set of equilibria: for a fixed discount factor, when all agents coordinate on what they perceive as the best equilibrium, there remain significant performance differences across dyads with different frames. Finally, we analyze some tensions between incremental versus radical changes in the cognitive frame