| Jörgen Weibull (Stockholm School of Economics). |
| Tenable blocks and settled equilibria |
| (with Roger Myerson) |
| Abstract When people interact in familiar settings, social conventions usually develop so that people tend to disregard alternatives outside the convention. 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 conventionally and rationally inside the block. We explore concepts that formalize this idea for finite normal-form games. Coarsely tenable blocks are product sets of pure strategies that have the above-mentioned robustness property. We call Nash equilibria with support in minimal such blocks coarsely settled. Finely tenable blocks are such that no player should prefer to deviate from the block when others are likely to act conventionally and rationally within it but otherwise would be likely to act rationally in the game as a whole. Equilibria with support in minimal such blocks we call finely settled. An equilibrium is fully settled if it is both coarsely and finely settled. We establish existence of fully settled equilibria in all finite games. Being proper, these equilibria induce sequential equilibria in all extensive-form games with the given normal form. For a generic class of normal-form games, our coarse and fine concepts are equivalent. |