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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.

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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0507001.

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Length: 25 pages
Date of creation: 02 Jul 2005
Date of revision: 06 Jul 2005
Handle: RePEc:wpa:wuwpga:0507001

Note: Type of Document - pdf; pages: 25
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Web page: http://128.118.178.162

Related research

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

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References

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  1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  2. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  3. Giuseppe Lopomo & Efe A Ok, 2004. "Bargaining, Interdependence and the Rationality of Fair Division," Levine's Bibliography 122247000000000395, UCLA Department of Economics.
  4. Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. S. Huck & J. Oechssler, 1996. "The Indirect Evolutionary Approach To Explaining Fair Allocations," SFB 373 Discussion Papers 1996,13, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Barry O'Neill, 1980. "A Problem of Rights Arbitration from the Talmud," Discussion Papers 445, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. 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.
  8. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  9. 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.
  10. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-77, May.
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