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Licensed Unlicensed Requires Authentication Published by De Gruyter August 7, 2020

Absence of Envy among “Neighbors” Can Be Enough

Chiara Donnini and Marialaura Pesce

Abstract

We assume that the set of agents is decomposed into several classes containing individuals related each other in some way, for example groups of neighbors. We propose a new definition of fairness by requiring efficiency and envy-freeness only within each group. We identify conditions under which absence of envy among “neighbors” is enough to ensure fairness in the entire society. We also show that equal-income Walrasian equilibria are the only fair allocations according to our notion, deriving as corollaries the equivalence theorems of Zhou (1992) and Cato (2010). The analysis is conducted in atomless economies as well as in mixed markets.


Corresponding author: Chiara Donnini, Dipartimento di Studi Aziendali e Quantitativi, Università degli Studi di Napoli Parthenope, Naples, Italy, E-mail:

Article note: We are grateful to the audience of the XXVII European Workshop on General Equilibrium Theory in Paris and RGEA workshop 2018 in Vigo, where previous versions of this paper were presented. A special thank goes to Daniela Puzzello (the Editor), the anonymous referees, Achille Basile and Maria Gabriella Graziano for their useful comments and suggestions.


References

Abebe, R., J. Kleinberg, and D. Parkes. 2017. “Fair Division via Social Comparison.” Proceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems, May 08–12, 2017, Sao Paulo, Brazil.Search in Google Scholar

Basile, A., R. Gilles, M. Graziano, and M. Pesce. 2020. “The Core of Economies with Collective Goods and a Social Division of Labor.” Economic Theory. https://doi.org/10.1007/s00199-020-01258-0.Search in Google Scholar

Basile, A., M. G. Graziano, and M. Pesce. 2016. “Oligopoly and Cost Sharing in Economies with Public Goods.” International Review of Economics 57: 487–506. https://doi.org/10.1111/iere.12165.Search in Google Scholar

Basile, A., M. G. Graziano, and C. Tarantino. 2017. “Coalitional Fairness with Participation Rates.” Journal of Economics. https://doi.org/10.1007/s00712–017–0543–7.Search in Google Scholar

Beynier, A., Y. Chevaleyre, L. Gourvs, N. Lesca, J. amd Maudet, and A. Wilczynski. 2018. “Local Envy-Freeness in House Allocation Problems.” Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems, July 10–15, 2018, Stockholm, Sweden.Search in Google Scholar

Cato, S. 2010. “Local Strict Envy-Freeness in Large Economies.” Mathematical Social Sciences 59: 319–22. https://doi.org/10.1016/j.mathsocsci.2010.01.002.Search in Google Scholar

Donnini, C., and M. Pesce. 2020. “Strict Fairness of Equilibria in Asymmetric Information Economies and Mixed Markets.” Economic Theory 69: 107–124. https://doi.org/10.1007/s00199-018-1158-0.Search in Google Scholar

Foley, D. 1967. “Resource Allocation and the Public Sector.” Yale Economic Essays 7: 45–98.Search in Google Scholar

Gabszewicz, J. J. 1975. “Coalitional Fairness of Allocations in Pure Exchange Economies.” Econometrica 43: 661–8. https://doi.org/10.2307/1913075.Search in Google Scholar

Gabszewicz, J. J., and J. Mertens. 1971. “An Equivalence Theorem for the Core of an Economy whose Atoms are Not “Too” Big.” Econometrica 39: 713–21. https://doi.org/10.2307/1909574.Search in Google Scholar

García-Cutrín, J., and C. Hervés-Beloso. 1993. “A Discrete Approach to Continuum Economies.” Economic Theory 3: 577–83. https://doi.org/10.1007/BF01209704.Search in Google Scholar

Greenberg, J., and B. Shitovitz. 1986. “A Simple Proof of the Equivalence Theorem for Oligopolistic Mixed Markets.” Journal of Mathematical Economics 15: 79–83. https://doi.org/10.1016/0304-4068(86)90001-7.Search in Google Scholar

Grodal, B. 1972. “A Second Remark on the Core of an Atomless Economy.” Econometrica 40: 581–3. https://doi.org/10.2307/1913187.Search in Google Scholar

Jackson, M. 2008. Social an economic networks. Princeton University Press.Search in Google Scholar

Shitovitz, B. 1973. “Oligopoly in Markets with a Continuum of Traders.” Econometrica 41: 467–501. https://doi.org/10.2307/1913371.Search in Google Scholar

Shitovitz, B. 1992. “Coalitional Fair Allocations in Smooth Mixed Markets with an Atomless Sector.” Mathematical Social Sciences 25: 27–40. https://doi.org/10.1016/0165-4896(92)90023-X.Search in Google Scholar

Thomson, W. 1982. “An Informationally Efficient Equity Criterion.” Journal of Public Economics 18: 243–63. https://doi.org/10.1016/0047-2727(82)90005-6.Search in Google Scholar

Thomson, W. 1988. “A Study of Choice Correspondences in Economies with a Variable Number of Agents.” Journal of Economic Theory 46: 237–54. https://doi.org/10.1016/0022-0531(88)90130-5.Search in Google Scholar

Varian, H. 1974. “Equity, Envy and Efficiency.” Journal of Economic Theory 9: 63–91. https://doi.org/10.1016/0022-0531(74)90075-1.Search in Google Scholar

Varian, H. 1976. “Two Problems in the Theory of Fairness.” Journal of Public Economics 5: 249–60. https://doi.org/10.1016/0047-2727(76)90018-9.Search in Google Scholar

Zhou, L. 1992. “Strictly Fair Allocations in Large Exchange Economies.” Journal of Economic Theory 57: 158–75. https://doi.org/10.1016/S0022-0531(05)80046-8.Search in Google Scholar

Received: 2020-02-06
Accepted: 2020-03-31
Published Online: 2020-08-07

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