K of them correspond to an agreement and the last one is the strategy pair where both players refuse to bargain.Įach of the K+1 equilibrium points can be the solution of the game.

The game has K+1 pure strategy equilibrium points. It is assumed that there is an indivisable smallest money unit. The model has the form of a ( K+1)×( K+1)-bimatrix game. One may think of an illegal deal where bargaining involves a risk of being punished - independently whether the deal is made or not. Thereby he avoids transaction costs c and d of bargaining which arise whether an agreement is reached or not. Otherwise both receive zero.Įach player i has a further alternative W i, namely not to bargain at all ( i=1, 2).

If agreement is reached player 2's payoffs is 1− x. The bargaining problem is the following one: the two bargainers - player 1 and player 2 - simultaneously and independently propose a payoff x of player 1 in the interval 〈0, 1〉. This theory selects one equilibrium point in every finite non-cooperative game. It is the purpose of the paper to analyse a bargeining situation with the help of the equilibrium selection theory of John C.

Deal or no deal game theory