On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms
研究一个猜想：对于大多数效用函数，博弈的纳什均衡只会产生有限种结果分布。作者给出了一个反例，证明当参与者不少于3人时该猜想不成立，并推广了一些已知结论。
Consider nonempty finite pure strategy sets S1,…,Sn, let S=S1×⋅⋅⋅×Sn, let Ω be a finite space of "outcomes," let Δ(Ω) be the set of probability distributions on Ω, and let θ: S→Δ(Ω) be a function. We study the conjecture that for any utility in a generic set of n-tuples of utilities on Ω there are finitely many distributions on Ω induced by the Nash equilibria of the game given by the induced utilities on S. We give a counterexample refuting the conjecture for n≥3. Several special cases of the conjecture follow from well known theorems, and we provide some generalizations of these results.