Consider a two-person bargaining game over a pie of size 1. Suppose that, initially, player 1 proposes an agreement which would give her utility , leaving player 2 with utility . In other words,...

Consider a two-person bargaining game over a pie of size 1. Suppose that, initially, player 1 proposes an agreement which would give her utility
, leaving player 2 with utility
. In other words, player 1 proposes point
 on their utility possibility frontier (UPF). In the meantime, player 2 has other ideas, proposing instead point
 [where
 and
. Let us now assume that, for each player, there is a maximum subjective probability of conflict (i.e. no agreement) that she can stand (i.e. if her estimate of conflict equals this probability, she is indifferent between acquiescing and holding firm). Moreover, assume that (a) the player with the lower maximum subjective probability of conflict concedes first, and (b) agreement implies that the two players’ maximum subjective probabilities of conflict are equal. Show that the players’ subjective probabilities of conflict are equalised only by the agreement corresponding to Nash’s solution of the bargaining problem. How do you interpret this result?