Uniform, Equal Division, and Other Envy-free Rules between the Two
This paper studies the problem of fairly allocating an amount of a divisible resource when preferences are single-peaked. We characterize the class of envy-free and peak-only rules and show that the class forms a complete lattice with respect to a dominance relation. We also pin down the subclass of strategy-proof rules and show that the subclass also forms a complete lattice. In both cases, the upper bound is the uniform rule, the lower bound is the equal division rule, and any other rule is between the two.
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- Roth, Alvin E. & Sotomayor, Marilda, 1992.
Handbook of Game Theory with Economic Applications,
in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541
- Chun, Youngsub, 2000. "Distributional properties of the uniform rule in economies with single-peaked preferences," Economics Letters, Elsevier, vol. 67(1), pages 23-27, April.
- Schummer, J. & Thomson, W., 1996.
"Two Derivations of the Uniform Rule and an Application to Bankruptcy,"
RCER Working Papers
423, University of Rochester - Center for Economic Research (RCER).
- Schummer, James & Thomson, William, 1997. "Two derivations of the uniform rule and an application to bankruptcy," Economics Letters, Elsevier, vol. 55(3), pages 333-337, September.
- Thomson, W., 1991. "Resource-Monotonic Solutions to the Problem of Fair Divosion when Preferences are Single-Peaked ," RCER Working Papers 301, University of Rochester - Center for Economic Research (RCER).
- Kesten, Onur, 2006. "More on the uniform rule: Characterizations without Pareto optimality," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 192-200, March.
- Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
- Bochet, Olivier & Sakai, Toyotaka, 2010. "Secure implementation in allotment economies," Games and Economic Behavior, Elsevier, vol. 68(1), pages 35-49, January.
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