Settled equilibria

When people recurrently interact in familiar settings, social conventions may develop so that people tend to disregard alternatives outside the conventional norm. For rational players to usually restrict attention to a block of conventional strategies, no player should prefer to deviate from the block when others are likely to act rationally and conventionally inside it. We explore concepts that formalize this idea for finite normal-form games. Settled equilibria are Nash equilibria with support in minimal blocks that can be conventionally accepted in such a sense. This refinement has a lot of cutting power in many games. It excludes some equilibria that meet other stringent refinements, for instance mixed equilibria of simple coordination games. We provide a psychological micro model for our approach and show that it implies a form of properness. We prove the general existence of settled equilibria. Since these are proper, they induce sequential equilibria in all extensive-form games with the given normal form. Thus, settled equilibrium is also a refinement of sequential equilibrium.