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The Game of Negotiations: Ordering Issues and Implementing Agreements

  • Lutz-Alexander Busch

    (University of Waterloo)

  • Ignatius Horstmann

    (University of Western Ontario)

We study a two-issue bargaining situation in which the surplus of one issue is public information, while that of the other issue is private information to one of the parties. Bargaining is by alternating offers under common time-discounting. The bargaining agenda is determined endogenously since players are free to offer on any number of outstanding issues. Offers must, however, be accepted or rejected in their entirety. Once an offer has been accepted it is not renegotiable. We study this game under two alternative rules for implementing agreements. In the first, partial agreements are implemented as they are reached, in the alternative setting implementation is joint, so that even if an offer on one issue is accepted consumption of this surplus is nevertheless delayed until the second issue is also settled. We show that the order in which issues are bargained in equilibrium is determined by three things: the implementation rule, the type of the informed player and the initial beliefs of the uninformed player. Specifically, an issue-by-issue bargaining agenda arises only when a low-valuation informed player faces an opponent who believes him to be likely a high-valuation type. In contrast to suggestions in the negotiation practitioner literature, such initial agenda offers always involve concessions (much smaller allocations to the informed player than in a bargain without agenda offers.) We also show that it is the implementation rule which determines which issue leads in the agenda. When implementation takes place as agreements are reached, then the issue of known size is negotiated first. If agreements are implemented only after all issues are settled, then, if order is relevant at all, large issues are settled first. All parties prefer the former rules of implementation to the latter.

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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1109.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1109
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  1. Admati, Anat R & Perry, Motty, 1987. "Strategic Delay in Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 345-64, July.
  2. Lutz-Alexander Busch & Ignatius J. Horstmann, 1999. "Signaling via an agenda in multi-issue bargaining with incomplete information," Economic Theory, Springer, vol. 13(3), pages 561-575.
  3. Sanford J. Grossman & Motty Perry, 1986. "Sequential Bargaining Under Asymmetric Information," NBER Technical Working Papers 0056, National Bureau of Economic Research, Inc.
  4. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  5. Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Fershtman, Chaim, 1990. "The importance of the agenda in bargaining," Games and Economic Behavior, Elsevier, vol. 2(3), pages 224-238, September.
  7. Rubinstein, Ariel, 1985. "A Bargaining Model with Incomplete Information about Time Preferences," Econometrica, Econometric Society, vol. 53(5), pages 1151-72, September.
  8. Busch, Lutz-Alexander & Horstmann, Ignatius, 1997. "A Comment on Issue-by-Issue Negotiations," Games and Economic Behavior, Elsevier, vol. 19(1), pages 144-148, April.
  9. Fershtman, Chaim, 2000. "A Note on Multi-Issue Two-Sided Bargaining: Bilateral Procedures," Games and Economic Behavior, Elsevier, vol. 30(2), pages 216-227, February.
  10. Inderst, Roman, 1998. "Multi-Issue Bargaining with Endogenous Agenda," Sonderforschungsbereich 504 Publications 98-35, Sonderforschungsbereich 504, Universit├Ąt Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  11. Busch, L-A. & Wen, Q., 1991. "Perfect Equilibria in a Negotiation Model," University of Western Ontario, The Centre for the Study of International Economic Relations Working Papers 9108, University of Western Ontario, The Centre for the Study of International Economic Relations.
  12. In-Koo Cho & David M. Kreps, 1997. "Signaling Games and Stable Equilibria," Levine's Working Paper Archive 896, David K. Levine.
  13. Fernandez, Raquel & Glazer, Jacob, 1991. "Striking for a Bargain between Two Completely Informed Agents," American Economic Review, American Economic Association, vol. 81(1), pages 240-52, March.
  14. Cho, In-Koo, 1987. "A Refinement of Sequential Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1367-89, November.
  15. Avery Christopher & Zemsky Peter B., 1994. "Money Burning and Multiple Equilibria in Bargaining," Games and Economic Behavior, Elsevier, vol. 7(2), pages 154-168, September.
  16. Bac, Mehmet & Raff, Horst, 1996. "Issue-by-Issue Negotiations: The Role of Information and Time Preference," Games and Economic Behavior, Elsevier, vol. 13(1), pages 125-134, March.
  17. Lang, Kevin & Rosenthal, Robert W, 2001. "Bargaining Piecemeal or All at Once?," Economic Journal, Royal Economic Society, vol. 111(473), pages 526-40, July.
  18. Drew Fudenberg & David K. Levine & Jean Tirole, 1985. "Infinite-Horizon Models of Bargaining with One-Sided Incomplete Information," Levine's Working Paper Archive 1098, David K. Levine.
  19. Weinberger, Catherine J., 2000. "Selective Acceptance and Inefficiency in a Two-Issue Complete Information Bargaining Game," Games and Economic Behavior, Elsevier, vol. 31(2), pages 262-293, May.
  20. Clara Ponsati & Joel Watson, 1998. "Multiple-Issue Bargaining and Axiomatic Solutions," International Journal of Game Theory, Springer, vol. 26(4), pages 501-524.
  21. Perry, Motty, 1986. "An Example of Price Formation in Bilateral Situations: A Bargaining Model with Incomplete Information," Econometrica, Econometric Society, vol. 54(2), pages 313-21, March.
  22. Jun, Byoung Heon, 1989. "Non-cooperative Bargaining and Union Formation," Review of Economic Studies, Wiley Blackwell, vol. 56(1), pages 59-76, January.
  23. Lutz-Alexander Bush & Shouyong Shi & Quan Wen, 1998. "Bargaining with Surplus Destruction," Canadian Journal of Economics, Canadian Economics Association, vol. 31(4), pages 915-932, November.
  24. Lutz-Alexander Busch & Ignatius Horstmann, 1999. "Endogenous Incomplete Contracts: A Bargaining Approach," Canadian Journal of Economics, Canadian Economics Association, vol. 32(4), pages 956-975, August.
  25. Haller, Hans & Holden, Steinar, 1990. "A letter to the editor on wage bargaining," Journal of Economic Theory, Elsevier, vol. 52(1), pages 232-236, October.
  26. Busch, Lutz-Alexander & Horstmann, Ignatius J, 1997. "Bargaining Frictions, Bargaining Procedures and Implied Costs in Multiple-Issue Bargaining," Economica, London School of Economics and Political Science, vol. 64(256), pages 669-80, November.
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