Jorgen Weibull
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.
Joint work with Roger Myerson.