Universality of Nash Components

Paper number: 12/05

Year: 2012

Source: 12/05

Paper Category: Discussion Paper


Dieter Balkenborg and Dries Vermeulen


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.

Universality of Nash Components Universality of Nash Components