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Learning to play games in extensive form by valuation

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  • Philippe Jehiel
  • Dov Samet

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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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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References

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  1. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  2. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  3. 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).
  4. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  5. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054.
  6. 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.
  7. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. G. Noldeke & L. Samuelson, 2010. "An Evolutionary Analysis of Backward and Forward Induction," Levine's Working Paper Archive 538, David K. Levine.
  9. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
  10. Philippe Jehiel & Dov Samet, 2006. "Valuation Equilibria," Levine's Bibliography 784828000000000111, UCLA Department of Economics.
  11. 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.
  12. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  13. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945.
  15. 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.
  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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Cited by:
  1. 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.
  2. Philippe Jehiel & Dov Samet, 2006. "Valuation Equilibria," Levine's Bibliography 784828000000000111, UCLA Department of Economics.
  3. Levine, David & Fudenberg, Drew, 2006. "Superstition and Rational Learning," Scholarly Articles 3196330, Harvard University Department of Economics.
  4. 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.
  5. Drew Fudenberg & David K Levine, 2006. "An Economists Perspective on Multi-Agent Learning," Levine's Working Paper Archive 784828000000000683, David K. Levine.

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