Non-Explanatory Equilibria: An Extremely Simple Game With (Mostly) Unattainable Fixed Points
Equilibrium analysis pervades mathematical social science. This paper calls into question the explanatory significance of equilibrium by offering an extremely simple game, most of whose equilibria are unattainable in principle from any of its initial conditions. Moreover, the number of computation steps required to reach those (few) equilibria that are attainable is shown to grow exponentially with the number of players--making long-run equilibrium a poor predictor of the gameâs observed state. The paper also poses a number of combinatorially challenging problems raised by the model.
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- John H. Nachbar, 1995.
"Prediction, Optimization, and Learning in Repeated Games,"
Game Theory and Information
9504001, EconWPA, revised 14 Feb 1996.
- John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
- John Nachbar, 2010. "Prediction, Optimization and Learning in Repeated Games," Levine's Working Paper Archive 576, David K. Levine.
- Prasad, Kislaya, 1997. "On the computability of Nash equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 943-953, June.
- Dean Foster & H Peyton Young, 1999.
"On the Impossibility of Predicting the Behavior of Rational Agents,"
Economics Working Paper Archive
423, The Johns Hopkins University,Department of Economics, revised Jun 2001.
- Dean P. Foster & H. Peyton Young, 2001. "On the Impossibility of Predicting the Behavior of Rational Agents," Working Papers 01-08-039, Santa Fe Institute.
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