A Social Foundation of Nash Bargaining Solution with Endogenous Bargaining Protocols

This paper provides a decentralized dynamic foundation of the Nash bargaining solution, which selects an outcome that maximizes the product of the individual gains over the disagreement outcome. Two agents are drawn from a large population and randomly matched to a partnership, if they successfully find an agreeable payoff vector. Abstracting away the details of a search and bargaining process, we model the search process for an agreeable outcome as a probability distribution over a feasible payoff vectors. In each period, the two agents choose to maintain or terminate the partnership, which is subject to a small exogenous probability of break down. As we regard the Nash bargaining solution as a steady state of a social dynamic, we focus on stationary undominated equilibrium. We show that as the discount factor converges to 1, and the probability of exogenous break down vanishes, the Nash bargaining solution emerges as a unique stationary undominated equilibrium outcome.