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Imitation Games and Computation

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TAn imitation game is a finite two person normal form game in which the two players have the same set of pure strategies and the goal of the second player is to choose the same pure strategy as the first player. Gale et al. (1950) gave a way of passing from a given two person game to a symmetric game whose symmetric Nash equilibria are in oneto-one correspondence with the Nash equilibria of the given game. We give a way of passing from a given symmetric two person game to an imitation game whose Nash equilibria are in one-to-one correspondence with the symmetric Nash equilibria of the given symmetric game. Lemke (1965) portrayed the Lemke-Howson algorithm as a special case of the Lemke paths algorithm. Using imitation games, we show how Lemke paths may be obtained by projecting Lemke-Howson paths.

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Paper provided by School of Economics, University of Queensland, Australia in its series Discussion Papers Series with number 359.

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Date of creation: 2008
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Handle: RePEc:qld:uq2004:359

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  1. Rahul Savani & Bernhard Stengel, 2006. "Hard-to-Solve Bimatrix Games," Econometrica, Econometric Society, Econometric Society, vol. 74(2), pages 397-429, 03.
  2. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(1), pages 80-93, March.
  3. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, Elsevier, vol. 63(2), pages 642-662, July.
  4. McLennan, Andrew & Tourky, Rabee, 2008. "Games in oriented matroids," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 807-821, July.
  5. McLennan, Andrew & Tourky, Rabee, 2010. "Simple complexity from imitation games," Games and Economic Behavior, Elsevier, Elsevier, vol. 68(2), pages 683-688, March.
  6. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, INFORMS, vol. 11(7), pages 681-689, May.
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