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Inducible Games: Using Tit-for-Tat to Stabilize Outcomes

Author

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  • Brams, Steven J.
  • Kilgour, D. Marc

Abstract

Assume it is known that one player in a 2 x 2 game can detect the strategy choice of its opponent with some probability before play commences. We formulate conditions under which the detector can, by credibly committing to a strategy of probabilistic tit-for-tat (based on its imperfect detector), induce an outcome favorable to itself. A non-Nash, Pareto-optimal outcome is inducible—that is, it can be stabilized via probabilistic tit-for-tat—in 20 of the 57 distinct 2 x 2 strict ordinal games without a mutually best outcome (35 percent). Sometimes the inducement is “weak,” but more often it is “strong.” As a case study, we consider the current conflict between Israel and Iran over Iran’s possible development of nuclear weapons and show that Israel’s credible commitment to probabilistic tit-for-tat can, with sufficiently accurate intelligence, induce a cooperative choice by Iran in one but not the other of two plausible games that model this conflict.

Suggested Citation

  • Brams, Steven J. & Kilgour, D. Marc, 2012. "Inducible Games: Using Tit-for-Tat to Stabilize Outcomes," MPRA Paper 41773, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41773
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    File URL: https://mpra.ub.uni-muenchen.de/41773/1/MPRA_paper_41773.pdf
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    References listed on IDEAS

    as
    1. Steven J. Brams & D. Marc Kilgour, 2009. "How Democracy Resolves Conflict in Difficult Games," Springer Series in Game Theory, in: Simon A. Levin (ed.), Games, Groups, and the Global Good, pages 229-241, Springer.
    2. Per Molander, 1985. "The Optimal Level of Generosity in a Selfish, Uncertain Environment," Journal of Conflict Resolution, Peace Science Society (International), vol. 29(4), pages 611-618, December.
    3. Simon A. Levin (ed.), 2009. "Games, Groups, and the Global Good," Springer Series in Game Theory, Springer, number 978-3-540-85436-4, March.
    4. Brams, Steven J., 2012. "Game Theory and the Humanities: Bridging Two Worlds," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262518252, December.
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    Cited by:

    1. Nasr, Eman S. & Kilgour, Marc D. & Noori, Hamid, 2015. "Strategizing niceness in co-opetition: The case of knowledge exchange in supply chain innovation projects," European Journal of Operational Research, Elsevier, vol. 244(3), pages 845-854.

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    More about this item

    Keywords

    2 x 2 games; tit-for-tat; inducubility; Israel-Iran conflict; nuclear weapons;
    All these keywords.

    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
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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