Bargaining and Bargaining Games

In this chapter, after specifying the bargaining problem à la Nash (1950), the Rubinstein gameRubinstein game and its subgame-perfect Nash equilibriumNash equilibrium are presented. The equilibrium is determined (1) by the shrinking of the cake to be distributed among the two players and (2) by how the shrinking is evaluated by the players. If players can make binding agreementsBinding agreement, then the self-enforcing power of the equilibrium is no longer needed. The players can jointly decide on feasible payoffs to serve as a bargaining outcome. The Nash solutionNash solution is the most prominent concept that supports such a decision; it is considered to be fair and reasonable. The Kalai-Smorodinsky solution is an alternative concept briefly discussed in the chapter. The Rubinstein gameRubinstein game and the Nash solutionNash solution “meet” in the Nash programNash program. More generally, the Nash programNash program asks for a non-cooperative game, like the Rubinstein gameRubinstein game, to produce outcomes as suggested by a cooperative game of the Nash solutionNash solution type. Of course, a non-cooperative game can result in cooperationCooperation.