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Lost in Translation? Basis Utility and Proportionality in Games

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  • Barry Feldman

    (Prism Analytics & DePaul University)

Abstract

Cooperative and noncooperative games have no representation of players's basis utilities. Basis utility is the natural reference point on a player's utility scale that enables the determination the marginal utility of any payoff or allocation. A player's basis utility can be determined by an observer and other players under standard rationality assumptions. Basis utility allows interpersonal comparison of proportional utility gains relative to the disagreement outcome. Proportional pure bargaining is the unique solution satisfying efficiency, symmetry, affine transformation invariance and monotonicity in pure bargaining games with basis utility. Characterization of the Nash (1950) bargaining solution requires the assumption of the irrelevance of basis utility in games with basis utility. All existing cooperative solution functions become translation invariant once proper account is taken of basis utility. The noncooperative rationality of these results is demonstrated with a proportional bargaining based on Gul (1988). Further noncooperative application is demonstrated by showing that quantal response equilibria with multiplicative error structures (Goeree, Holt and Palfrey (2004)) become translation invariant with specification of basis utility.

Suggested Citation

  • Barry Feldman, 2005. "Lost in Translation? Basis Utility and Proportionality in Games," Game Theory and Information 0507001, University Library of Munich, Germany, revised 28 Feb 2006.
  • Handle: RePEc:wpa:wuwpga:0507001
    Note: Type of Document - pdf; pages: 25
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0507/0507001.pdf
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    References listed on IDEAS

    as
    1. Lopomo, Giuseppe & Ok, Efe A, 2001. "Bargaining, Interdependence, and the Rationality of Fair Division," RAND Journal of Economics, The RAND Corporation, vol. 32(2), pages 263-283, Summer.
    2. Huck, Steffen & Oechssler, Jorg, 1999. "The Indirect Evolutionary Approach to Explaining Fair Allocations," Games and Economic Behavior, Elsevier, vol. 28(1), pages 13-24, July.
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    4. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    5. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    6. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-777, May.
    7. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    8. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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    More about this item

    Keywords

    Basis utility; equal split; Kalai-Smorodinsky solution; Nash bargaining; quantal response equilibria; proportional bargaining; translation invariance.;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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