Elasticity of Games
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.
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- R. Aumann, 2010.
"Correlated Equilibrium as an expression of Bayesian Rationality,"
513, UCLA Department of Economics.
- Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
- Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
- 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.
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