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Learning To Play Games In Extensive Form By Valuation

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  • Philippe Jehiel
  • Dov Samet

Abstract

Game theoretic models of learning which are based on the strategic form of the game cannot explain learning in games with large extensive form. We study learning in such games by using valuation of moves. A valuation for a player is a numeric assessment of her moves that purports to reflect their desirability. We consider a myopic player, who chooses moves with the highest valuation. Each time the game is played, the player revises her valuation by assigning the payoff obtained in the play to each of the moves she has made. We show for a repeated win-lose game that if the player has a winning strategy in the stage game, there is almost surely a time after which she always wins. When a player has more than two payoffs, a more elaborate learning procedure is required. We consider one that associates with each move the average payoff in the rounds in which this move was made. When all players adopt this learning procedure, with some perturbations, then, with probability 1 there is a time after which strategies that are close to subgame perfect equilibrium are played. A single player who adopts this procedure can guarantee only her individually rational payoff.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

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  • Philippe Jehiel & Dov Samet, 2010. "Learning To Play Games In Extensive Form By Valuation," Levine's Working Paper Archive 391749000000000034, David K. Levine.
  • Handle: RePEc:cla:levarc:391749000000000034
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    Cited by:

    1. Jehiel, Philippe & Samet, Dov, 2007. "Valuation equilibrium," Theoretical Economics, Econometric Society, vol. 2(2), June.
    2. Ran Spiegler, 2016. "Bayesian Networks and Boundedly Rational Expectations," The Quarterly Journal of Economics, Oxford University Press, vol. 131(3), pages 1243-1290.
    3. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    4. Drew Fudenberg & David K Levine, 2006. "An Economists Perspective on Multi-Agent Learning," Levine's Working Paper Archive 784828000000000683, David K. Levine.
    5. Drew Fudenberg & David K. Levine, 2006. "Superstition and Rational Learning," American Economic Review, American Economic Association, vol. 96(3), pages 630-651, June.
    6. Lambson, Val & van den Berghe, John, 2015. "Skill, complexity, and strategic interaction," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 516-530.
    7. Florian Herold, 2012. "Carrot or Stick? The Evolution of Reciprocal Preferences in a Haystack Model," American Economic Review, American Economic Association, vol. 102(2), pages 914-940, April.
    8. Naoki Funai, 2019. "Convergence results on stochastic adaptive learning," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 907-934, November.
    9. Wichardt, Philipp C., 2012. "Existence of valuation equilibria when equilibrium strategies cannot differentiate between equal ties," Games and Economic Behavior, Elsevier, vol. 74(2), pages 709-713.
    10. Oyarzun, Carlos & Sarin, Rajiv, 2013. "Learning and risk aversion," Journal of Economic Theory, Elsevier, vol. 148(1), pages 196-225.
    11. Wichardt, Philipp C., 2010. "Modelling equilibrium play as governed by analogy and limited foresight," Games and Economic Behavior, Elsevier, vol. 70(2), pages 472-487, November.
    12. Philippe Jehiel & Juni Singh, 2019. "Multi-state choices with aggregate feedback on unfamiliar alternatives," PSE Working Papers halshs-02183444, HAL.
    13. Yoav Shoham & Rob Powers & Trond Grenager, 2006. "If multi-agent learning is the answer, what is the question?," Levine's Working Paper Archive 122247000000001156, David K. Levine.

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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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