Universality of Nash components
University of Exeter Economics Department Discussion Papers Series 12/05
We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game—a common interest game whose common payoff to the players is at most equal to one—whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi- algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets. We discuss implications of our results for the strategic stability of success sets, and apply the results to construct a Nash component with index k for any fixed integer k.
An updated version of this working paper was subsequently published and is available at http://hdl.handle.net/10871/17592