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Compensatory Transfers in Two-Player Decision Problems

  • Green, Jerry

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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File URL: http://dash.harvard.edu/bitstream/handle/1/3204680/green_compensatory.pdf
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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, 1984. "Egalitarianisme and utilitarianism in quasi-linear bargaining," CEPREMAP Working Papers (Couverture Orange) 8417, CEPREMAP.
  2. Moulin, Herve, 1989. "Monotonic surplus sharing: Characterization results," Games and Economic Behavior, Elsevier, vol. 1(3), pages 250-274, September.
  3. 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.
  4. 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.
  5. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
  6. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
  7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  8. 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.
  9. 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.
  10. E. Loehman & A. Whinston, 1974. "An Axiomatic Approach to Cost Allocation for Public Investment," Public Finance Review, , vol. 2(2), pages 236-250, April.
  11. Thomson, A., 1989. "The Consistency Principle," RCER Working Papers 192, University of Rochester - Center for Economic Research (RCER).
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