Generic finiteness of outcome distributions for two-person game forms with three outcomes

Abstract

A two-person game form is given by nonempty finite sets S 1 , S 2 of pure strategies, a nonempty set Ω of outcomes, and a function θ : S 1 × S 2 → Δ ( Ω ) , where Δ ( Ω ) is the set of probability measures on Ω . We prove that if the set of outcomes contains just three elements, generically, there are finitely many distributions on Ω induced by Nash equilibria.