Bargaining in a long-term relationship and the Rubinstein solution

In a recent paper, Muthoo (1995) discusses whether the Rubinstein solution carries over on repeated bargaining situations. He concludes that stationary equilibria for such a repeated bargaining game do not imply the Rubinstein solution and that several non-stationary equilibria may exist. This paper demonstrates that the Rubinstein solution applies not only to unique bargaining problems but to repeated bargaining problems as well. It demonstrates that stationarity holds also in Muthoo's model, and it shows that a certain result of Muthoo which makes the split of bargaining gains independent of the discount factors is no relevant case as the discounted sum of each agent's utility is infinite. The paper introduces an alternative approach which takes into account that offers may cover also future realizations by employing future contracts. It shows that the agreement depends crucially on the enforceability of contracts if bargaining behavior fulfils a rationality condition.