Elasticity of Games
AbstractWe 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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Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp592.
Length: 19 pages
Date of creation: Dec 2011
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-12-13 (All new papers)
- NEP-GTH-2011-12-13 (Game Theory)
- NEP-HPE-2011-12-13 (History & Philosophy of Economics)
- NEP-MIC-2011-12-13 (Microeconomics)
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- Aumann, Robert J, 1987.
"Correlated Equilibrium as an Expression of Bayesian Rationality,"
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.
- R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
- 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.
- Gilad Bavly, 2012. "Uncertainty in the Traveler's Dilemma," Discussion Paper Series dp595, The Center for the Study of Rationality, Hebrew University, Jerusalem.
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