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Imitation games and computation

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  • McLennan, Andrew
  • Tourky, Rabee

Abstract

An 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. We explain how, in two different settings, observations obtained from imitation games complete a circle of ideas, showing that phenomena that had for many years seemed to be distinct are actually superficially different manifestations of a single structure. First, one can pass from a given two person finite game to an imitation game whose Nash equilibria are in one-to-one correspondence with the Nash equilibria of the given game. Second, each of the paths of the procedure described in Lemke (1965) for solving a linear complementarity problem is the projection of the path of the Lemke-Howson algorithm applied to an imitation game.

Suggested Citation

  • McLennan, Andrew & Tourky, Rabee, 2010. "Imitation games and computation," Games and Economic Behavior, Elsevier, vol. 70(1), pages 4-11, September.
    • Handle: RePEc:eee:gamebe:v:70:y:2010:i:1:p:4-11
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    References listed on IDEAS

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    1. McLennan, Andrew & Tourky, Rabee, 2008. "Games in oriented matroids," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 807-821, July.
    2. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
    3. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    4. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    5. Rahul Savani & Bernhard Stengel, 2006. "Hard-to-Solve Bimatrix Games," Econometrica, Econometric Society, vol. 74(2), pages 397-429, March.
    6. McLennan, Andrew & Tourky, Rabee, 2010. "Simple complexity from imitation games," Games and Economic Behavior, Elsevier, vol. 68(2), pages 683-688, March.
    7. Walter D. Morris, 1994. "Lemke Paths on Simple Polytopes," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 780-789, November.
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    Cited by:

    1. Rahul Savani & Bernhard von Stengel, 2016. "Unit vector games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 7-27, March.

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