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Testing Threats in Repeated Games

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  • Ran Spiegler

Abstract

I introduce a solution concept for infinite-horizon games, called “Nash equilibrium with added tests”, in which players optimize with respect to relevant threats only after having tested them before. Both the optimal response and the tests are part of equilibrium behavior. The concept is applied to repeated 2×2 games and yields the following results: 1) Sustained cooperation in games such as the Prisoner’s Dilemma is preceded by a “build up” phase, whose comparative statics are characterized. 2) Sustainability of long-run cooperation by means of familiar selfenforcement conventions varies with the payoff structure. E.g., “constructive reciprocity” achieves cooperation with minimal buildup time in the Prisoner’s Dilemma, yet it is inconsistent with long-run cooperation in Chicken. 3) Nevertheless, a “folk theorem” holds for this class of games.
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Suggested Citation

  • Ran Spiegler, 2002. "Testing Threats in Repeated Games," NajEcon Working Paper Reviews 391749000000000445, www.najecon.org.
    • Handle: RePEc:cla:najeco:391749000000000445
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    1. is not listed on IDEAS
    2. Ran Spiegler, 2025. "Machine-Learning to Trust," Papers 2507.10363, arXiv.org, revised Nov 2025.
    3. Hubie Chen, 2013. "Bounded rationality, strategy simplification, and equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 593-611, August.
    4. Ran Spiegler, 2006. "The Market for Quacks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1113-1131.
    5. Irene C. L. Ng & Lu‐Ming Tseng, 2008. "Learning to be Sociable: The Evolution of Homo Economicus," American Journal of Economics and Sociology, Wiley Blackwell, vol. 67(2), pages 265-286, April.
    6. Mathevet, Laurent, 2018. "An axiomatization of plays in repeated games," Games and Economic Behavior, Elsevier, vol. 110(C), pages 19-31.

    More about this item

    JEL classification:

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

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