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A non-cooperative bargaining theory with incomplete information: Verifiable types

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  • Okada, Akira

Abstract

We consider a non-cooperative sequential bargaining game with incomplete information where two players negotiate for mechanisms with ex post verifiable types at the interim stage. We prove the existence of a stationary sequential equilibrium of the bargaining game where the ex post Nash bargaining solution with no delay is asymptotically implemented with probability one. Further, the ex post Nash bargaining solution is a unique outcome of a stationary equilibrium under the property of Independence of Irrelevant Types (IIT), whereby the response of every type of a player is independent of allocations proposed to his other types, and under a self-selection property of their belief.

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  • Okada, Akira, 2016. "A non-cooperative bargaining theory with incomplete information: Verifiable types," Journal of Economic Theory, Elsevier, vol. 163(C), pages 318-341.
    • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:318-341
    DOI: 10.1016/j.jet.2016.02.002
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    1. Myerson, Roger B, 1983. "Mechanism Design by an Informed Principal," Econometrica, Econometric Society, vol. 51(6), pages 1767-1797, November.
    2. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    3. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    4. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    5. de Clippel, Geoffroy & Minelli, Enrico, 2004. "Two-person bargaining with verifiable information," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 799-813, November.
    6. Rubinstein, Ariel, 1985. "A Bargaining Model with Incomplete Information about Time Preferences," Econometrica, Econometric Society, vol. 53(5), pages 1151-1172, September.
    7. Grossman, Sanford J. & Perry, Motty, 1986. "Perfect sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 39(1), pages 97-119, June.
    8. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    9. Maskin, Eric & Tirole, Jean, 1990. "The Principal-Agent Relationship with an Informed Principal: The Case of Private Values," Econometrica, Econometric Society, vol. 58(2), pages 379-409, March.
    10. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    11. Kalyan Chatterjee & Larry Samuelson, 1987. "Bargaining with Two-sided Incomplete Information: An Infinite Horizon Model with Alternating Offers," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(2), pages 175-192.
    12. Ausubel, Lawrence M. & Cramton, Peter & Deneckere, Raymond J., 2002. "Bargaining with incomplete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 50, pages 1897-1945, Elsevier.
    13. Robert Wilson, 2005. "Information, efficiency, and the core of an economy," Studies in Economic Theory, in: Dionysius Glycopantis & Nicholas C. Yannelis (ed.), Differential Information Economies, pages 55-64, Springer.
    14. Myerson, Roger B, 1984. "Two-Person Bargaining Problems with Incomplete Information," Econometrica, Econometric Society, vol. 52(2), pages 461-487, March.
    15. Grossman, Sanford J. & Perry, Motty, 1986. "Sequential bargaining under asymmetric information," Journal of Economic Theory, Elsevier, vol. 39(1), pages 120-154, June.
    16. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    17. John C. Harsanyi, 1968. "Games with Incomplete Information Played by "Bayesian" Players Part II. Bayesian Equilibrium Points," Management Science, INFORMS, vol. 14(5), pages 320-334, January.
    18. Okada, Akira, 2012. "Non-cooperative bargaining and the incomplete informational core," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1165-1190.
    19. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    20. Mylovanov, Timofiy & Troger, Thomas E., 2012. "Informed principal problems in generalized private values environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
    21. Farrell Joseph, 1993. "Meaning and Credibility in Cheap-Talk Games," Games and Economic Behavior, Elsevier, vol. 5(4), pages 514-531, October.
    22. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
    23. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 179-221.
    24. Drew Fudenberg & Jean Tirole, 1983. "Sequential Bargaining with Incomplete Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(2), pages 221-247.
    25. John Sutton, 1986. "Non-Cooperative Bargaining Theory: An Introduction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 709-724.
    26. Maskin, Eric & Tirole, Jean, 1992. "The Principal-Agent Relationship with an Informed Principal, II: Common Values," Econometrica, Econometric Society, vol. 60(1), pages 1-42, January.
    27. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-1348, November.
    28. Okada, Akira, 2010. "The Nash bargaining solution in general n-person cooperative games," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2356-2379, November.
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    Cited by:

    1. Akira Okada, 2015. "Cooperation and Institution in Games," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 1-32, March.
    2. Geoffroy de Clippel & Jack Fanning & Kareen Rozen, 2022. "Bargaining over Contingent Contracts under Incomplete Information," American Economic Review, American Economic Association, vol. 112(5), pages 1522-1554, May.
    3. Akira Okada, 2018. "Incomplete Contract and Verifiability," KIER Working Papers 982, Kyoto University, Institute of Economic Research.
    4. Kristal K. Trejo & Ruben Juarez & Julio B. Clempner & Alexander S. Poznyak, 2023. "Non-Cooperative Bargaining with Unsophisticated Agents," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 937-974, March.

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    More about this item

    Keywords

    Bayesian bargaining problem; Incomplete information; Mechanism selection; Ex post Nash bargaining solution; Non-cooperative games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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