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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 666156000000000046.

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Date of creation: 12 Jun 2003
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Handle: RePEc:cla:levrem:666156000000000046

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

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References

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  1. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
  2. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  3. Jehiel, Philippe & Samet, Dov, 2005. "Learning to play games in extensive form by valuation," Journal of Economic Theory, Elsevier, vol. 124(2), pages 129-148, October.
  4. Piccione, Michele & Rubinstein, Ariel, 1997. "On the Interpretation of Decision Problems with Imperfect Recall," Games and Economic Behavior, Elsevier, vol. 20(1), pages 3-24, July.
  5. Philippe Jeniel, 2001. "Analogy-Based Expectation Equilibrium," Economics Working Papers 0003, Institute for Advanced Study, School of Social Science.
  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. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  8. 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.
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Cited by:
  1. Philippe Jehiel & Dov Samet, 2010. "Learning To Play Games In Extensive Form By Valuation," Levine's Working Paper Archive 391749000000000034, David K. Levine.
  2. 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.
  3. Mohlin, Erik, 2009. "Optimal Categorization," Working Paper Series in Economics and Finance 721, Stockholm School of Economics, revised 08 Jul 2009.
  4. 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.
  5. Jakub Steiner & Colin Stewart, 2012. "Price Distortions in High-Frequency Markets," Discussion Papers 1549, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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