Solid outcomes in finite games

Abstract

A new solution concept for finite games is presented and analyzed. It is defined in terms of outcomes—probability distributions over the plays of the game. Solid outcomes are robust to the representation of the game, whether in normal or extensive form, and are consistent with backward induction. They are also unaffected by the removal or addition of dominated strategies. Solid outcome sets exist in all finite extensive-form games with perfect recall. They have support in minimal “game blocks,” a class of product sets of pure-strategy profiles that are robust set-valued candidates for conventions and social norms in recurrent population play of the game. Algorithms for identifying all solid outcomes are presented, and simulations illustrate the solution concept's significant cutting power and computational efficiency.