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Learning to play games in extensive form by valuation

  • Philippe Jehiel
  • Dov Samet

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.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 391749000000000040.

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Date of creation: 09 Dec 2010
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Handle: RePEc:cla:levarc:391749000000000040
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  1. Ebbe Hendon & Hans Jørgen Jacobsen & Birgitte Sloth, . "Fictitious Play in Extensive Form Games," Discussion Papers 94-06, University of Copenhagen. Department of Economics.
  2. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, June.
  3. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
  4. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  5. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  6. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Noeldecke,Georg & Samuelson,Larry, . "An evolutionary analysis of backward and forward induction," Discussion Paper Serie B 228, University of Bonn, Germany.
  8. 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.
  9. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  10. Jehiel, Philippe & Samet, Dov, 2007. "Valuation equilibrium," Theoretical Economics, Econometric Society, vol. 2(2), June.
  11. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  12. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. 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).
  14. Sarin, Rajiv & Vahid, Farshid, 1999. "Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 28(2), pages 294-309, August.
  15. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  16. 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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