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Valuation Equilibria

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  • Philippe Jehiel
  • Dov Samet

Abstract

We introduce a new solution concept for games in extensive form with perfect information: the valuation equilibrium. The moves of each player are partitioned into similarity classes. A valuation of the player is a real valued function on the set of her similarity classes. At each node a player chooses a move that belongs to a class with maximum valuation. The valuation of each player is \emph{consistent} with the strategy profile in the sense that the valuation of a similarity class is the player expected payoff given that the path (induced by the strategy profile) intersects the similarity class. The solution concept is applied to decision problems and multi-player extensive form games. It is contrasted with existing solution concepts. An aspiration-based approach is also proposed, in which the similarity partitions are determined endogenously. The corresponding equilibrium is called the aspiration-based valuation equilibrium (ASVE). While the Subgame Perfect Nash Equilibrium is always an ASVE, there are other ASVE in general. But, in zero-sum two-player games without chance moves every player must get her value in any ASVE.

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Bibliographic Info

Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 784828000000000111.

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Date of creation: 08 Feb 2006
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Handle: RePEc:cla:levrem:784828000000000111

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Web page: http://www.dklevine.com/

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  1. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  2. Philippe Jehiel, 2005. "Analogy-Based Expectation Equilibrium," Levine's Bibliography 784828000000000106, UCLA Department of Economics.
  3. Philippe Jehiel & Dov Samet, 2010. "Learning to play games in extensive form by valuation," Levine's Working Paper Archive 391749000000000040, David K. Levine.
  4. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
  5. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July.
  6. Jakub Steiner & Colin Stewart, 2007. "Learning by Similarity in Coordination Problems," CERGE-EI Working Papers wp324, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
  7. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
  8. Rubinstein, Ariel, 1995. "On the Interpretation of Decision Problems with Imperfect Recall," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 324-324, December.
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Cited by:
  1. Philippe Jehiel & Dov Samet, 2001. "Learning To Play Games In Extensive Form By Valuation," NajEcon Working Paper Reviews 391749000000000010, www.najecon.org.
  2. Mohlin, Erik, 2009. "Optimal Categorization," Working Paper Series in Economics and Finance 721, Stockholm School of Economics, revised 08 Jul 2009.
  3. 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.
  4. Steiner, Jakub & Stewart, Colin, 2014. "Price Distortions in High-Frequency Markets," CEPR Discussion Papers 9817, C.E.P.R. Discussion Papers.
  5. Seel, Christian & Wichardt, Philipp C., 2012. "How burning money requires a lot of rationality to be effective," Economics Letters, Elsevier, vol. 115(1), pages 111-113.
  6. Vessela Daskalova & Nicolaas J. Vriend, 2014. "Categorization and Coordination," Working Papers 719, Queen Mary, University of London, School of Economics and Finance.

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