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Learning to play games in extensive form by valuation

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  • Jehiel, Philippe
  • Samet, Dov

Abstract

A valuation for a board game is an assignment of numeric values to different states of the board. The valuation reflects the desirability of the states for the player. It can be used by a player to decide on her next move during the play. We assume a myopic player, who chooses a move with the highest valuation. Valuations can also be revised, and hopefully improved, after each play of the game. Here, a very simple valuation revision is considered, in which the states of the board visited in a play are assigned the payoff obtained in the play. We show that by adopting such a learning process a player who has a winning strategy in a win-lose game can almost surely guarantee a win in a repeated game. When a player has more than two payoffs, a more elaborate learning procedure is required. We consider one that associates with each state the average payoff in the rounds in which this node was reached. When all players adopt this learning procedure, with some perturbations, then, with probability 1, strategies that are close to subgame perfect equilibrium are played after some time. A single player who adopts this procedure can guarantee only her individually rational payoff.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 124 (2005)
Issue (Month): 2 (October)
Pages: 129-148

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Handle: RePEc:eee:jetheo:v:124:y:2005:i:2:p:129-148

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
  2. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, December.
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  5. Philippe Jehiel & Dov Samet, 2003. "Valuation Equilibria," Game Theory and Information 0310003, EconWPA.
  6. Karandikar, Rajeeva & Mookherjee, Dilip & Ray, Debraj & Vega-Redondo, Fernando, 1998. "Evolving Aspirations and Cooperation," Journal of Economic Theory, Elsevier, vol. 80(2), pages 292-331, June.
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  10. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
  11. Cho, In-Koo & Matsui, Akihiko, 2005. "Learning aspiration in repeated games," Journal of Economic Theory, Elsevier, vol. 124(2), pages 171-201, October.
  12. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
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Cited by:
  1. Drew Fudenberg & David K. Levine, 2006. "Superstition and Rational Learning," American Economic Review, American Economic Association, vol. 96(3), pages 630-651, June.
  2. 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 914-40, April.
  3. Drew Fudenberg & David K Levine, 2006. "An Economists Perspective on Multi-Agent Learning," Levine's Working Paper Archive 784828000000000683, David K. Levine.
  4. Philippe Jehiel & Dov Samet, 2003. "Valuation Equilibria," Levine's Bibliography 666156000000000046, UCLA Department of Economics.
  5. Ran Spiegler, 2014. "Bayesian Networks and Boundedly Rational Expectations," Discussion Papers 1417, Centre for Macroeconomics (CFM).
  6. 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.
  7. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
  8. 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.
  9. 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.
  10. Oyarzun, Carlos & Sarin, Rajiv, 2013. "Learning and risk aversion," Journal of Economic Theory, Elsevier, vol. 148(1), pages 196-225.

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