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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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Citations

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Cited by:
  1. Oyarzun, Carlos & Sarin, Rajiv, 2013. "Learning and risk aversion," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(1), pages 196-225.
  2. 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.
  3. Florian Herold, 2012. "Carrot or Stick? The Evolution of Reciprocal Preferences in a Haystack Model," American Economic Review, American Economic Association, American Economic Association, vol. 102(2), pages 914-40, April.
  4. Wichardt, Philipp C., 2010. "Modelling equilibrium play as governed by analogy and limited foresight," Games and Economic Behavior, Elsevier, Elsevier, vol. 70(2), pages 472-487, November.
  5. Friederike Mengel, 2007. "Learning Across Games," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2007-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. Drew Fudenberg & David K Levine, 2005. "Superstition and Rational Learning," Levine's Working Paper Archive 618897000000000731, David K. Levine.
  7. Ran Spiegler, 2014. "Bayesian Networks and Boundedly Rational Expectations," Discussion Papers 1417, Centre for Macroeconomics (CFM).
  8. Drew Fudenberg & David K Levine, 2006. "An Economists Perspective on Multi-Agent Learning," Levine's Working Paper Archive 784828000000000683, David K. Levine.
  9. Wichardt, Philipp C., 2012. "Existence of valuation equilibria when equilibrium strategies cannot differentiate between equal ties," Games and Economic Behavior, Elsevier, Elsevier, vol. 74(2), pages 709-713.
  10. Philippe Jehiel & Dov Samet, 2003. "Valuation Equilibria," Levine's Bibliography 666156000000000046, UCLA Department of Economics.

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