Semi-algebraic sets and equilibria of binary games

Guillaume Vigeral (1) , Yannick Viossat (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Any nonempty, compact, semi-algebraic set in [0, 1] n is the projection of the set of mixed equilibria of a finite game with 2 actions per player on its first n coordinates. A similar result follows for sets of equilibrium payoffs. The proofs are constructive and elementary.

Mots clés: semi-algebraic sets; Nash equilibria; equilibrium payoffs; binary games

Domaines: Optimisation et contrôle [math.OC]

Guillaume Vigeral, Yannick Viossat. Semi-algebraic sets and equilibria of binary games. Operations Research Letters, 2016, 44, pp.19-24. ⟨10.1016/j.orl.2015.11.002⟩. ⟨hal-01252923⟩