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Compensatory Transfers in Two-Player Decision Problems

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  • Green, Jerry

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 compensationâ€. 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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Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3204680.

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Date of creation: 2005
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Publication status: Published in International Journal of Game Theory
Handle: RePEc:hrv:faseco:3204680

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  1. Moulin, Herve, 1989. "Monotonic surplus sharing: Characterization results," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(3), pages 250-274, September.
  2. Moulin, Herve, 1985. "Egalitarianism and Utilitarianism in Quasi-linear Bargaining," Econometrica, Econometric Society, Econometric Society, vol. 53(1), pages 49-67, January.
  3. Thomson, A., 1989. "The Consistency Principle," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 192, University of Rochester - Center for Economic Research (RCER).
  4. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, Elsevier, vol. 31(2), pages 211-226, December.
  5. Tadenuma, Koichi & Thomson, William, 1993. "The fair allocation of an indivisible good when monetary compensations are possible," Mathematical Social Sciences, Elsevier, Elsevier, vol. 25(2), pages 117-132, February.
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  7. Elster, Jon, 1991. "Local justice : How institutions allocate scarce goods and necessary burdens," European Economic Review, Elsevier, Elsevier, vol. 35(2-3), pages 273-291, April.
  8. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(1), pages 120-148, June.
  9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, Econometric Society, vol. 18(2), pages 155-162, April.
  10. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 195-213, August.
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Cited by:
  1. Geoffroy de Clippel & Camelia Bejan, 2009. "No Profitable Decomposition in Quasi-Linear Allocation Problems," Working Papers, Brown University, Department of Economics 2009-6, Brown University, Department of Economics.
  2. Yuan Ju, 2013. "Efficiency and compromise: a bid-offer–counteroffer mechanism with two players," International Journal of Game Theory, Springer, Springer, vol. 42(2), pages 501-520, May.

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