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Aspirational Bargaining

Author

Listed:
  • Lones Smith

    (The University of Michigan)

  • Ennio Stacchetti

    (The University of Michigan)

Abstract

This paper offers a noncooperative behaviourally-founded solution of the complete information bargaining problem where two impatient individuals wish to divide a unit pie. We formulate the game in continuous time, with unrestricted timing and content of offers. Reprising experimental work from 1960, we introduce and explore aspirational equilibrium -- a Markovian refinement of subgame perfection where behaviour is governed by aspiration values (expected payoffs). The analysis is tractable, and generates many intuitive aspects of bargaining absent from the standard temporal monopoly paradigm: wars of attrition explains delay; serious offers are concessions; offers may be turned down, strictly disappointing the proposers, or accepted, strictly helping the proposer. In particular, an endogenous `proposee' advantage arises, as opposed to the hard-wired proposer standard advantage. We find that discounted aspiration values form a martingale, and thereby compute bounds on the expected bargaining duration from observed offers. We also deduce some simple implications about consecutive offers, and relate delay times, offers, and acceptance rates. Finally, we draw into question a traditional comparative static: Ceteris paribus, more impatient players can expect more of the pie.

Suggested Citation

  • Lones Smith & Ennio Stacchetti, 2002. "Aspirational Bargaining," Game Theory and Information 0201003, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0201003
    Note: Type of Document - Adobe acrobat [pdf]; prepared on IBM PC; to print on HP/PostScript; pages: 32 ; figures: included
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0201/0201003.pdf
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    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Dilip Abreu & Faruk Gul, 2000. "Bargaining and Reputation," Econometrica, Econometric Society, vol. 68(1), pages 85-118, January.
    3. Karandikar, Rajeeva & Mookherjee, Dilip & Ray, Debraj & Vega-Redondo, Fernando, 1998. "Evolving Aspirations and Cooperation," Journal of Economic Theory, Elsevier, vol. 80(2), pages 292-331, June.
    4. David Schmeidler & Itzhak Gilboa, 1994. "Reaction to Price Changes and Aspiration Level Adjustments," Working Papers 023, Ohio State University, Department of Economics.
    5. Stahl, Dale II, 1993. "Strategic choice of waiting and reaction times in bargaining," Economics Letters, Elsevier, vol. 43(1), pages 31-34.
    6. Dilip Abreu & David Pearce, 2003. "A Behavioral Model of Bargaining with Endogenous Types," Cowles Foundation Discussion Papers 1446, Cowles Foundation for Research in Economics, Yale University.
    7. Simon, Leo K & Stinchcombe, Maxwell B, 1989. "Extensive Form Games in Continuous Time: Pure Strategies," Econometrica, Econometric Society, vol. 57(5), pages 1171-1214, September.
    8. Drew Fudenberg & Jean Tirole, 1985. "Preemption and Rent Equalization in the Adoption of New Technology," Review of Economic Studies, Oxford University Press, vol. 52(3), pages 383-401.
    9. Bergin, James & MacLeod, W Bentley, 1993. "Continuous Time Repeated Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 21-37, February.
    10. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
    11. Sakovics Jozsef, 1993. "Delay in Bargaining Games with Complete Information," Journal of Economic Theory, Elsevier, vol. 59(1), pages 78-95, February.
    12. Perry Motty & Reny Philip J., 1993. "A Non-cooperative Bargaining Model with Strategically Timed Offers," Journal of Economic Theory, Elsevier, vol. 59(1), pages 50-77, February.
    13. Fershtman Chaim & Seidmann Daniel J., 1993. "Deadline Effects and Inefficient Delay in Bargaining with Endogenous Commitment," Journal of Economic Theory, Elsevier, vol. 60(2), pages 306-321, August.
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    Cited by:

    1. Dilip Abreu & David Pearce, 2003. "A Behavioral Model of Bargaining with Endogenous Types," Cowles Foundation Discussion Papers 1446, Cowles Foundation for Research in Economics, Yale University.
    2. Christopher Tyson, 2010. "Dominance solvability of dynamic bargaining games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 457-477, June.
    3. Yildiz, Muhamet, 2003. "Walrasian bargaining," Games and Economic Behavior, Elsevier, vol. 45(2), pages 465-487, November.
    4. Dilip Abreu & David G. Pearce, 2006. "Bargaining, Reputation and Equilibrium Selection in Repeated Games with Contracts," Levine's Bibliography 321307000000000640, UCLA Department of Economics.
    5. Gilat Levy & Ronny Razin, 2004. "It Takes Two: An Explanation for the Democratic Peace," Journal of the European Economic Association, MIT Press, vol. 2(1), pages 1-29, March.

    More about this item

    Keywords

    subgame perfect equilibrium; aspiration; extensive form;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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