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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. Sergiu Hart, 1999. "Evolutionary Dynamics and Backward Induction," Game Theory and Information 9905002, EconWPA, revised 23 Mar 2000.
  2. Philippe Jehiel & Dov Samet, 2003. "Valuation Equilibria," Levine's Bibliography 666156000000000046, UCLA Department of Economics.
  3. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
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  5. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  6. Noeldecke,Georg & Samuelson,Larry, . "An evolutionary analysis of backward and forward induction," Discussion Paper Serie B 228, University of Bonn, Germany.
  7. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
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  9. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "Fictitious Play in Extensive Form Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 177-202, August.
  10. Debraj Ray & Dilip Mookherjee & Fernando Vega Redondo & Rajeeva L. Karandikar, 1996. "Evolving aspirations and cooperation," Working Papers. Serie AD 1996-06, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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  13. Cho, In-Koo & Matsui, Akihiko, 2005. "Learning aspiration in repeated games," Journal of Economic Theory, Elsevier, vol. 124(2), pages 171-201, October.
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Citations

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Cited by:
  1. 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.
  2. Jehiel, Philippe & Samet, Dov, 2007. "Valuation equilibrium," Theoretical Economics, Econometric Society, vol. 2(2), June.
  3. Drew Fudenberg & David K. Levine, 2006. "Superstition and Rational Learning," American Economic Review, American Economic Association, vol. 96(3), pages 630-651, June.
  4. Oyarzun, Carlos & Sarin, Rajiv, 2013. "Learning and risk aversion," Journal of Economic Theory, Elsevier, vol. 148(1), pages 196-225.
  5. 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.
  6. Fudenberg, Drew & Levine, David, 2007. "An Economist's Perspective on Multi-Agent Learning," Scholarly Articles 3200613, Harvard University Department of Economics.
  7. 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.
  8. 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.
  9. Friederike Mengel, 2007. "Learning Across Games," Working Papers. Serie AD 2007-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  10. Ran Spiegler, 2014. "Bayesian Networks and Boundedly Rational Expectations," Discussion Papers 1417, Centre for Macroeconomics (CFM).

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