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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, valuation equilibrium, which is based on a partition of each player's moves into similarity classes. A valuation of a player is a real-valued function on the set of her similarity classes. In this equilibrium each player's strategy is optimal in the sense that at each of her nodes, a player chooses a move that belongs to a class with maximum valuation. The valuation of each player is consistent with the strategy profile in the sense that the valuation of a similarity class is the player's 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. The valuation approach is next applied to stopping games, in which non-terminal moves form a single similarity class, and we note that the behaviors obtained echo some biases observed experimentally. Finally, we tentatively suggest a way of endogenizing the similarity partitions in which moves are categorized according to how well they perform relative to the expected equilibrium value, interpreted as the aspiration level.

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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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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. Philippe Jehiel & Dov Samet, 2010. "Learning to play games in extensive form by valuation," Levine's Working Paper Archive 391749000000000040, David K. Levine.
  3. Philippe Jeniel, 2001. "Analogy-Based Expectation Equilibrium," Economics Working Papers 0003, Institute for Advanced Study, School of Social Science.
  4. Rubinstein, Ariel, 1995. "On the Interpretation of Decision Problems with Imperfect Recall," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 324-324, December.
  5. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  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. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
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Cited by:
  1. Steiner, Jakub & Stewart, Colin, 2014. "Price Distortions in High-Frequency Markets," CEPR Discussion Papers 9817, C.E.P.R. Discussion Papers.
  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. Vessela Daskalova & Nicolaas J. Vriend, 2014. "Categorization and Coordination," Working Papers 719, Queen Mary, University of London, School of Economics and Finance.
  4. Philippe Jehiel & Dov Samet, 2010. "Learning To Play Games In Extensive Form By Valuation," Levine's Working Paper Archive 391749000000000034, David K. Levine.
  5. 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.
  6. Mohlin, Erik, 2014. "Optimal categorization," Journal of Economic Theory, Elsevier, vol. 152(C), pages 356-381.

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