Mixed-strategy equilibria in the Nash Demand Game
研究了纳什需求博弈中混合策略均衡的条件，发现玩家需求集合必须平衡，并完整刻画了双方期望收益均为正时的均衡，结果可用于离散公共品的私人提供。
In the Nash Demand Game, each of the two players announces the share he demands of an amount of money that may be split between them. If the demands can be satisfied, they are; otherwise, neither player receives any money. This game has many pure-strategy equilibria. This paper characterizes mixed-strategy equilibria. The condition critical for an equilibrium is that players’ sets of possible demands be balanced. Two sets of demands are balanced if each demand in one set can be matched with a demand in the other set such that they sum to one. For Nash’s original game, a complete characterization is given of the equilibria in which both players’ expected payoffs are strictly positive. The findings are applied to the private provision of a discrete public good.