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Non-Explanatory Equilibria: An Extremely Simple Game With (Mostly) Unattainable Fixed Points

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  • Joshua M. Epstein
  • Ross A. Hammond

Abstract

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.

Suggested Citation

  • Joshua M. Epstein & Ross A. Hammond, 2001. "Non-Explanatory Equilibria: An Extremely Simple Game With (Mostly) Unattainable Fixed Points," Working Papers 01-08-043, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:01-08-043
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    References listed on IDEAS

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    1. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
    2. 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.
    3. Prasad, Kislaya, 1997. "On the computability of Nash equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 943-953, June.
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    Keywords

    Mathematical social science; game theory equilibrium; explanation; attainability;

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