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.
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- John Sutton, 1986. "Non-Cooperative Bargaining Theory: An Introduction," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 709-724.
- Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March.
- Evans, Robert & Maskin, Eric, 1989. "Efficient renegotiation--proof equilibria in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 361-369, December.
- Rubinstein, Ariel, 1982.
"Perfect Equilibrium in a Bargaining Model,"
Econometric Society, vol. 50(1), pages 97-109, January.
- Joseph Farrell and Eric Maskin., 1987.
"Renegotiation in Repeated Games,"
Economics Working Papers
8759, University of California at Berkeley.
- Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-64, November.
- Akira Okada, 1986. "A Two-Person Repeated Bargaining Game with Long-Term Contracts," Discussion Papers 706, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Muthoo Abhinay, 1995. "Bargaining in a Long-Term Relationship with Endogenous Termination," Journal of Economic Theory, Elsevier, vol. 66(2), pages 590-598, August.
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