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Valuation equilibrium

Author

Listed:
  • Jehiel, Philippe

    () (PSE and UCL)

  • Samet, Dov

    () (Tel Aviv University)

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.

Suggested Citation

  • Jehiel, Philippe & Samet, Dov, 2007. "Valuation equilibrium," Theoretical Economics, Econometric Society, vol. 2(2), June.
  • Handle: RePEc:the:publsh:187
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    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20070163/1206/53
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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.
    3. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    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, pages 81-104.
    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. 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.
    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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    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. David Ettinger & Philippe Jehiel, 2010. "A Theory of Deception," American Economic Journal: Microeconomics, American Economic Association, pages 1-20.
    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. Lambson, Val & van den Berghe, John, 2015. "Skill, complexity, and strategic interaction," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 516-530.
    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.
    6. Ignacio Esponda & Demian Pouzo, 2014. "Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models," Papers 1411.1152, arXiv.org, revised May 2016.
    7. Ignacio Esponda & Demian Pouzo, 2015. "Equilibrium in Misspecified Markov Decision Processes," Papers 1502.06901, arXiv.org, revised May 2016.
    8. 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.
    9. 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.
    10. 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.
    11. Steiner, Jakub & Stewart, Colin, 2015. "Price distortions under coarse reasoning with frequent trade," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 574-595.
    12. Vessela Daskalova & Nicolaas J. Vriend, 2014. "Categorization and Coordination," Working Papers 719, Queen Mary University of London, School of Economics and Finance.

    More about this item

    Keywords

    Game theory; bounded rationality; valuation; similarity; aspiration;

    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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