Commitments to threat strategies in Nash bargaining
If a normal form game is given, the players can follow two different courses of action: they can bargain on the set of feasible payoffs or they can play the game non-cooperatively. A combination of both approaches is also possible. First the players choose a so-called threat strategy that will be played if bargaining is not successful. Then the players try to find a way out by bargaining. If bargaining is successful, the results of the negotiation form the payoffs. If not, the threat strategies are implemented and produce the payoffs. In the present paper the players are free to commit themselves to threat strategies or not. If they refuse to choose a threat strategy, they are free to choose their strategy after the failure of the bargaining phase. For two-person games it is shown that there is an equilibrium of this game where both players choose to commit and agree upon the Nash bargaining solution during the negotiations (a solution equilibrium). For three-person games the authors give an example in which there is no solution equilibrium. In this example it is crucial that the players announce their commitment before the threat strategy is chosen. If the choice of commitment and the choice of the threat strategy is done without announcing the commitment decision (so the players do not know which players will commit to a threat strategy when they choose their threat strategy) this difference disappears.
scientific article; zbMATH DE number 429108