Mixed-strategy equilibria in the Nash demand game (Q611997)

This paper presents an equilibrium analysis in the Nash demand game. In this game, two players have the opportunity to divide an amount of money between them and simultaneously announce their demanded shares of the money. If both demands can be satisfied, then they are; otherwise neither player receives anything. The Nash demand game admits (uncountably) many pure-strategy equilibria. In particular, there exist equilibria in which the available amount of money is fully distributed to the players. The only pure-strategy equilibrium in undominated strategies yielding disagreement has each player demand the full amount. However, empirical research seems to show that such kind of disagreement does not match the observations of disagreement in the experiments. Previous literature shows instead that disagreement arise as a failure of the players to coordinate on a pure-strategy equilibrium. Hence disagreement might naturally arise in the play of a mixed-strategy equilibrium. This paper addresses the question (raised in previous literature) to characterize mixed-strategy equilibria in the Nash demand game. The author identifies the key condition for an equilibrium in mixed strategies: players' sets of possible demands must 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 the full amount of money. Conversely if the demand sets are balanced, additional conditions guarantee that there exists a mixed-strategy equilibrium in which players completely randomize over their demand sets.