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Compensatory transfers in two-player decision problems

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  • Jerry Green

Abstract

This paper presents an axiomatic characterization of a family of solutions to two-player quasi-linear social choice problems. In these problems the players select a single action from a set available to them. They may also transfer money between themselves. The solutions form a one-parameter family, where the parameter is a non-negative number, t . The solutions can be interpreted as follows: Any efficient action can be selected. Based on this action, compute for each player a “best claim for compensation†. A claim for compensation is the difference between the value of an alternative action and the selected efficient action, minus a penalty proportional to the extent to which the alternative action is inefficient. The coefficient of proportionality of this penalty is t . The best claim for compensation for a player is the maximum of this computed claim over all possible alternative actions. The solution, at the parameter value t , is to implement the chosen efficient action and make a monetary transfer equal to the average of these two best claims. The characterization relies on three main axioms. The paper presents and justifies these axioms and compares them to related conditions used in other bargaining contexts. In Nash Bargaining Theory, the axioms analogous to these three are in conflict with each other. In contrast, in the quasi-linear social choice setting of this paper, all three conditions can be satisfied simultaneously.
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  • Jerry Green, 2005. "Compensatory transfers in two-player decision problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 159-180, June.
  • Handle: RePEc:spr:jogath:v:33:y:2005:i:2:p:159-180
    DOI: 10.1007/s00182-005-0200-1
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    1. Hervé Moulin, 1987. "The Pure Compensation Problem: Egalitarianism Versus Laissez-Fairism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 769-783.
    2. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038.
    3. Moulin, Herve, 1985. "Egalitarianism and Utilitarianism in Quasi-linear Bargaining," Econometrica, Econometric Society, vol. 53(1), pages 49-67, January.
    4. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    5. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. Thomson, A., 1989. "The Consistency Principle," RCER Working Papers 192, University of Rochester - Center for Economic Research (RCER).
    8. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
    9. Youngsub Chun, 2000. "Agreement, separability, and other axioms for quasi-linear social choice problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 507-521.
    10. Elster, Jon, 1991. "Local justice : How institutions allocate scarce goods and necessary burdens," European Economic Review, Elsevier, vol. 35(2-3), pages 273-291, April.
    11. CHAMPSAUR, Paul, 1975. "How to share the cost of a public good?," LIDAM Reprints CORE 268, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Kaneko, Mamoru, 1977. "The ratio equilibrium and a voting game in a public goods economy," Journal of Economic Theory, Elsevier, vol. 16(2), pages 123-136, December.
    13. E. Loehman & A. Whinston, 1974. "An Axiomatic Approach to Cost Allocation for Public Investment," Public Finance Review, , vol. 2(2), pages 236-250, April.
    14. Moulin, Herve, 1989. "Monotonic surplus sharing: Characterization results," Games and Economic Behavior, Elsevier, vol. 1(3), pages 250-274, September.
    15. Myerson, Roger B, 1981. "Utilitarianism, Egalitarianism, and the Timing Effect in Social Choice Problems," Econometrica, Econometric Society, vol. 49(4), pages 883-897, June.
    16. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. 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.
    18. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
    19. Tadenuma, Koichi & Thomson, William, 1993. "The fair allocation of an indivisible good when monetary compensations are possible," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 117-132, February.
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