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Elasticity of Games

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  • Gilad Bavly

Abstract

We develop an elasticity index of a strategic game. The index measures the robustness of the set of rational outcomes of a game. The elasticity index of a game is the maximal ratio between the change of the rational outcomes and the size of an infinitesimal perturbation. The perturbation is on the players’ knowledge of the game. The elasticity of a strategic game is a nonnegative number. A small elasticity is indicative of the robustness of the rational outcomes (for example, if there is only one player the elasticity is 0), and a large elasticity is indicative of non-robustness. For example, the elasticity of the (normalized) n-stage finitely repeated prisoner’s dilemma is at least exponential in n, as is the elasticity of the n-stage centipede game and the n-ranged traveler’s dilemma. The concept of elasticity enables us to look from a different perspective at Neyman’s (1999) repeated games when the number of repetitions is not commonly known, and Aumann’s (1992) demonstration of the effect of irrationality perturbations.

Suggested Citation

  • Gilad Bavly, 2011. "Elasticity of Games," Discussion Paper Series dp592, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp592
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    References listed on IDEAS

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    1. Abraham Neyman, 1999. "Cooperation in Repeated Games when the Number of Stages is Not Commonly Known," Econometrica, Econometric Society, vol. 67(1), pages 45-64, January.
    2. Robert J. Aumann, 2025. "Correlated Equilibrium as an Expression of Bayesian Rationality," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 7, pages 175-200, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Gilad Bavly, 2017. "Uncertainty in the traveler’s dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 1-12, March.

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