Coalitional Bargaining Games with Random Proposers: Theory and Application

We consider a noncooperative coalitional bargaining game with random proposers. In a general case that the recognition probability is arbitrary anｄplayers have different discount factors for future payoffs, the existence of a stationary subgame perfect equilibrium (SSPE) is proved, and the condition for the grand coalition to be formed is provided. We also prove that the grand-coalition SSPE is a unique symmetric SSPE for any discount factor in a symmetric game with nonempty core. In the last part of the paper, we apply the bargaining model to a production economy with one employer and multiple workers. When players are sufficiently patient, the economy has a unique SSPE payoff. The equilibrium allocation is compared with cooperative solutions such as the core, the Shapley value and the nucleolus. The SSPE payoff and the nucleolus have similar distributional properties.