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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.

Suggested Citation

  • Philippe Jehiel & Dov Samet, 2003. "Valuation Equilibria," Game Theory and Information 0310003, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0310003
    Note: Type of Document - ; pages: 18
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. 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.
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    4. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    5. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    6. 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.
    7. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945.
    8. Jakub Steiner & Colin Stewart, 2007. "Learning by Similarity in Coordination Problems," CERGE-EI Working Papers wp324, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    9. 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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    Citations

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    Cited by:

    1. David Ettinger & Philippe Jehiel, 2010. "A Theory of Deception," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 1-20, February.
    2. Mohlin, Erik, 2014. "Optimal categorization," Journal of Economic Theory, Elsevier, vol. 152(C), pages 356-381.
    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. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    5. Mohlin, Erik & Östling, Robert & Wang, Joseph Tao-yi, 2020. "Learning by similarity-weighted imitation in winner-takes-all games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 225-245.
    6. Daskalova, Vessela & Vriend, Nicolaas J., 2021. "Learning frames," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 78-96.
    7. Lambson, Val & van den Berghe, John, 2015. "Skill, complexity, and strategic interaction," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 516-530.
    8. 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.
    9. Jehiel, Philippe & Singh, Juni, 2021. "Multi-state choices with aggregate feedback on unfamiliar alternatives," Games and Economic Behavior, Elsevier, vol. 130(C), pages 1-24.
    10. Ignacio Esponda & Demian Pouzo, 2014. "Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models," Papers 1411.1152, arXiv.org, revised Nov 2019.
    11. Ignacio Esponda & Demian Pouzo, 2015. "Equilibrium in Misspecified Markov Decision Processes," Papers 1502.06901, arXiv.org, revised May 2016.
    12. 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.
    13. Pe[combining cedilla]ski, Marcin, 2011. "Prior symmetry, similarity-based reasoning, and endogenous categorization," Journal of Economic Theory, Elsevier, vol. 146(1), pages 111-140, January.
    14. 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.
    15. Rampal, Jeevant, 2022. "Limited Foresight Equilibrium," Games and Economic Behavior, Elsevier, vol. 132(C), pages 166-188.
    16. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
    17. Steiner, Jakub & Stewart, Colin, 2015. "Price distortions under coarse reasoning with frequent trade," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 574-595.

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    More about this item

    Keywords

    bounded rationality; valuation; similarity; aspiration.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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