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Optimism and commitment: an elementary theory of bargaining and war

  • Clara Ponsati

    ()

  • Santiago Sanchez-Pages

    ()

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.

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File URL: http://hdl.handle.net/10.1007/s13209-011-0073-4
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Article provided by Spanish Economic Association in its journal SERIEs.

Volume (Year): 3 (2012)
Issue (Month): 1 (March)
Pages: 157-179

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Handle: RePEc:spr:series:v:3:y:2012:i:1:p:157-179
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  1. Powell, Robert, 1996. "Bargaining in the Shadow of Power," Games and Economic Behavior, Elsevier, vol. 15(2), pages 255-289, August.
  2. Garfinkel, Michelle R. & Skaperdas, Stergios (ed.), 2012. "The Oxford Handbook of the Economics of Peace and Conflict," OUP Catalogue, Oxford University Press, number 9780195392777, March.
  3. Powell, Robert, 2006. "War as a Commitment Problem," International Organization, Cambridge University Press, vol. 60(01), pages 169-203, January.
  4. Matthew O. Jackson & Massimo Morelli, 2007. "Political Bias and War," American Economic Review, American Economic Association, vol. 97(4), pages 1353-1373, September.
  5. Santiago Sánchez-Pagés, 2009. "Conflict as a Part of the Bargaining Process," Economic Journal, Royal Economic Society, vol. 119(539), pages 1189-1207, 07.
  6. Carmen Bevia & Luis C. Corchon, 2008. "Peace agreements without commitment," Economics Working Papers we081508, Universidad Carlos III, Departamento de Economía.
  7. Alastair Smith & Allan C. Stam, 2004. "Bargaining and the Nature of War," Journal of Conflict Resolution, Peace Science Society (International), vol. 48(6), pages 783-813, December.
  8. Darren Filson & Suzanne Werner, . "A Bargaining Model of War and Peace: Anticipating the Onset, Duration, and Outcome of War," Claremont Colleges Working Papers 2001-02, Claremont Colleges.
  9. Fearon, James D., 1995. "Rationalist explanations for war," International Organization, Cambridge University Press, vol. 49(03), pages 379-414, June.
  10. Helmut Bester & Karl Wärneryd, 2006. "Conflict and the Social Contract," Scandinavian Journal of Economics, Wiley Blackwell, vol. 108(2), pages 231-249, 07.
  11. Santiago Sanchez-Pages, 2009. "Bargaining and Conflict with Incomplete Information," ESE Discussion Papers 191, Edinburgh School of Economics, University of Edinburgh.
  12. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-99, March.
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