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Optimism and commitment: An elementary theory of bargaining and war

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  • Ponsati, Clara
  • Sanchez-Pages, Santiago

Abstract

We propose an elementary theory of wars fought by fully rational contenders. Two parties play a Markov game that combines stages of bargaining with stages where one side has the ability to impose surrender on the other. Under uncertainty and incomplete information, in the unique equilibrium of the game, long confrontations occur: war arises when reality disappoints initial (rational) optimism, and it persist longer when both agents are optimists but reality proves both wrong. Bargaining proposals that are rejected initially might eventually be accepted after several periods of confrontation. We provide an explicit computation of the equilibrium, evaluating the probability of war, and its expected losses as a function of i) the costs of confrontation, ii) the asymmetry of the split imposed under surrender, and iii) the strengths of contenders at attack and defense. Changes in these parameters display non-monotonic effects.

Suggested Citation

  • Ponsati, Clara & Sanchez-Pages, Santiago, 2010. "Optimism and commitment: An elementary theory of bargaining and war," SIRE Discussion Papers 2010-101, Scottish Institute for Research in Economics (SIRE).
  • Handle: RePEc:edn:sirdps:232
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    File URL: http://hdl.handle.net/10943/232
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    References listed on IDEAS

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    1. Santiago Sánchez-Pagés, 2009. "Conflict as a Part of the Bargaining Process," Economic Journal, Royal Economic Society, vol. 119(539), pages 1189-1207, July.
    2. Powell, Robert, 1996. "Bargaining in the Shadow of Power," Games and Economic Behavior, Elsevier, vol. 15(2), pages 255-289, August.
    3. Santiago Sanchez-Pages, 2009. "Bargaining and Conflict with Incomplete Information," ESE Discussion Papers 191, Edinburgh School of Economics, University of Edinburgh.
    4. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-399, March.
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    6. Beviá, Carmen & Corchón, Luis C., 2010. "Peace agreements without commitment," Games and Economic Behavior, Elsevier, vol. 68(2), pages 469-487, March.
    7. Darren Filson & Suzanne Werner, "undated". "A Bargaining Model of War and Peace: Anticipating the Onset, Duration, and Outcome of War," Claremont Colleges Working Papers 2001-02, Claremont Colleges.
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    12. Helmut Bester & Karl Wärneryd, 2006. "Conflict and the Social Contract," Scandinavian Journal of Economics, Wiley Blackwell, vol. 108(2), pages 231-249, July.
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    14. Powell, Robert, 2006. "War as a Commitment Problem," International Organization, Cambridge University Press, vol. 60(01), pages 169-203, January.
    15. Matthew O. Jackson & Massimo Morelli, 2007. "Political Bias and War," American Economic Review, American Economic Association, vol. 97(4), pages 1353-1373, September.
      • Jackson, Matthew O. & Morelli, Massimo, "undated". "Political bias and war," Working Papers 1247, California Institute of Technology, Division of the Humanities and Social Sciences.
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    More about this item

    Keywords

    bargaining; incomplete information; commitment; war;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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