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The endgame

Author

Listed:
  • Banerjee, Anurag N.
  • Markovich, Sarit
  • Seccia, Giulio

Abstract

On December 1st, 2009 President Obama announced that the U.S. troops would have started leaving Afghanistan on July 2011. Rather than simply waiting “the U.S. troops out,” the Taliban forces responded with a spike in attacks followed by a decline as the withdrawal date approached. These, at first, counter-intuitive phenomena, are addressed by studying a two-player, zero-sum game where the duration of the strategic interaction is either known or unknown (i.e., the game can stop at any time with positive probability). We find that, conditional on the players' relative position, players' equilibrium strategies are non-stationary in a known duration game but they are stationary in the unknown duration case. Hence, introducing uncertainty, no matter how small, changes players' optimal behavior qualitatively and discontinuously: qualitatively because their behavior becomes stationary; discontinuously because the equilibrium is stationary only as far as the continuation probability is bounded away from 1.

Suggested Citation

  • Banerjee, Anurag N. & Markovich, Sarit & Seccia, Giulio, 2019. "The endgame," Games and Economic Behavior, Elsevier, vol. 118(C), pages 176-192.
    • Handle: RePEc:eee:gamebe:v:118:y:2019:i:c:p:176-192
    DOI: 10.1016/j.geb.2019.08.010
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    1. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    2. Walker, Mark & Wooders, John & Amir, Rabah, 2011. "Equilibrium play in matches: Binary Markov games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 487-502, March.
    3. Kathryn E. Spier, 1992. "The Dynamics of Pretrial Negotiation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 93-108.
    4. Hans K. Hvide, 2002. "Tournament Rewards and Risk Taking," Journal of Labor Economics, University of Chicago Press, vol. 20(4), pages 877-898, October.
    5. González-Díaz, Julio & Palacios-Huerta, Ignacio, 2016. "Cognitive performance in competitive environments: Evidence from a natural experiment," Journal of Public Economics, Elsevier, vol. 139(C), pages 40-52.
    6. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    7. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    8. Jeffrey Ely & Alexander Frankel & Emir Kamenica, 2015. "Suspense and Surprise," Journal of Political Economy, University of Chicago Press, vol. 123(1), pages 215-260.
    9. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    10. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
    11. Subhasish Chowdhury & Oliver Gürtler, 2015. "Sabotage in contests: a survey," Public Choice, Springer, vol. 164(1), pages 135-155, July.
    12. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    13. Luís M. B. Cabral, 2003. "R&D Competition when firms Choose Variance," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 12(1), pages 139-150, March.
    14. Sundaram, Rangarajan K., 1989. "Perfect equilibrium in non-randomized strategies in a class of symmetric dynamic games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 153-177, February.
    15. Anurag N. Banerjee & Sarit Markovich & Giulio Seccia, 2016. "The Endgame," Working Papers 1601, Nazarbayev University, Department of Economics.
    16. Muhamet Yildiz, 2011. "Bargaining with Optimism," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 451-478, September.
    17. Engle-Warnick, Jim & Slonim, Robert L., 2004. "The evolution of strategies in a repeated trust game," Journal of Economic Behavior & Organization, Elsevier, vol. 55(4), pages 553-573, December.
    18. Barry J. Nalebuff & Joseph E. Stiglitz, 1983. "Prices and Incentives: Towards a General Theory of Compensation and Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 21-43, Spring.
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    More about this item

    Keywords

    Stochastic games; Information; Conflict resolution;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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