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

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Author Info
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.

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Paper provided by Santa Fe Institute in its series Working Papers with number 01-08-043.

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Date of creation: Aug 2001
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Handle: RePEc:wop:safiwp:01-08-043

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Keywords: Mathematical social science game theory equilibrium explanation attainability

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  1. Prasad, Kislaya, 1997. "On the computability of Nash equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 943-953, June. [Downloadable!] (restricted)
  2. 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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This page was last updated on 2008-7-29.


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