Computing dominance-based solution concepts

Two common criticisms of Nash equilibrium are its dependence on very demanding epistemic assumptions and its computational intractability. We study the computational properties of less demanding set-valued solution concepts that are based on varying notions of dominance. These concepts are intuitively appealing, they always exist, and admit unique minimal solutions in important subclasses of games. Examples include Shapley's saddles, Harsanyi and Selten's primitive formations, Basu and Weibull's CURB sets, and Dutta and Laslier's minimal covering sets. We propose two generic algorithms for computing these concepts and investigate for which classes of games and which properties of the underlying dominance notion the algorithms are sound and efficient.