Escalation game with endogenous demands and the Nash bargaining solution

Abstract

The paper examines the behavior of two agents who need to make a joint decision but they have conflicting preferences about the choice of the outcome. Conventionally such problem is considered as the bargaining problem described as the situation of dividing a pie. But we introduce the model that sheds a different light on the problem in question. The problem is described as the conflict situation modelled as a two-stage game. In the first stage players propose outcomes. The settlement is made if the proposed outcomes are the same. If not, the game moves onto the second stage where they play the concession game called the escalation game. In the escalation game, each player, in turn, has the choice between either to submit by accepting the other's demand or to escalate by way of insisting his demand to be accepted. Each escalation generates a probability of disagrement outcome. There are two main findings: (1) it is shown that the player's decision is determined by his risk limit which measures his intensity towards winning. (2) it is shown that there is a path of disagreement probabilities in which proposing the Nash cooperative solution is the optimal strategy for both players.