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Solidarity to achieve stability

Author

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  • Alcalde-Unzu, Jorge
  • Gallo, Oihane
  • Inarra, Elena
  • Moreno-Ternero, Juan D.

Abstract

Agents may form coalitions. Each coalition shares its endowment among its agents by applying a sharing rule. The sharing rule induces a coalition formation problem by assuming that agents rank coalitions according to the allocation they obtain in the corresponding sharing problem. We characterize the sharing rules that induce a class of stable coalition formation problems as those that satisfy a natural axiom that formalizes the principle of solidarity. Thus, solidarity becomes a sufficient condition to achieve stability.

Suggested Citation

  • Alcalde-Unzu, Jorge & Gallo, Oihane & Inarra, Elena & Moreno-Ternero, Juan D., 2024. "Solidarity to achieve stability," European Journal of Operational Research, Elsevier, vol. 315(1), pages 368-377.
  • Handle: RePEc:eee:ejores:v:315:y:2024:i:1:p:368-377
    DOI: 10.1016/j.ejor.2023.11.034
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    as
    1. Perry, Motty & Reny, Philip J, 1994. "A Noncooperative View of Coalition Formation and the Core," Econometrica, Econometric Society, vol. 62(4), pages 795-817, July.
    2. Alcalde-Unzu, Jorge & Gómez-Rúa, María & Molis, Elena, 2015. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Games and Economic Behavior, Elsevier, vol. 90(C), pages 134-150.
    3. H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
    4. Oihane Gallo & Bettina Klaus, 2022. "Stable partitions for proportional generalized claims problems," Cahiers de Recherches Economiques du Département d'économie 22.03, Université de Lausanne, Faculté des HEC, Département d’économie.
    5. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954, December.
    6. John E. Roemer, 1986. "Equality of Resources Implies Equality of Welfare," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 751-784.
    7. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    8. Stovall, John E., 2014. "Asymmetric parametric division rules," Games and Economic Behavior, Elsevier, vol. 84(C), pages 87-110.
    9. Ambec, Stefan & Sprumont, Yves, 2002. "Sharing a River," Journal of Economic Theory, Elsevier, vol. 107(2), pages 453-462, December.
    10. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    11. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    12. Grabisch, Michel & Funaki, Yukihiko, 2012. "A coalition formation value for games in partition function form," European Journal of Operational Research, Elsevier, vol. 221(1), pages 175-185.
    13. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2022. "Monotonicity in sharing the revenues from broadcasting sports leagues," European Journal of Operational Research, Elsevier, vol. 297(1), pages 338-346.
    14. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    15. Bas J. Dietzenbacher & Aleksei Y. Kondratev, 2023. "Fair and Consistent Prize Allocation in Competitions," Management Science, INFORMS, vol. 69(6), pages 3319-3339, June.
    16. Moreno-Ternero, Juan D. & Vidal-Puga, Juan, 2021. "Aggregator operators for dynamic rationing," European Journal of Operational Research, Elsevier, vol. 288(2), pages 682-691.
    17. Juan D Moreno-Ternero & John E Roemer, 2006. "Impartiality, Priority, and Solidarity in the Theory of Justice," Econometrica, Econometric Society, vol. 74(5), pages 1419-1427, September.
    18. Moreno-Ternero, Juan D. & Roemer, John E., 2012. "A common ground for resource and welfare egalitarianism," Games and Economic Behavior, Elsevier, vol. 75(2), pages 832-841.
    19. Moulin, Herve, 1987. "Egalitarian-Equivalent Cost Sharing of a Public Good," Econometrica, Econometric Society, vol. 55(4), pages 963-976, July.
    20. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    21. M. Puy, 2013. "Stable coalition governments: the case of three political parties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 65-87, January.
    22. Hakan İnal, 2015. "Core of coalition formation games and fixed-point methods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 745-763, December.
    23. Gallo, Oihane & Inarra, Elena, 2018. "Rationing rules and stable coalition structures," Theoretical Economics, Econometric Society, vol. 13(3), September.
    24. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
    25. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    26. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    27. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
    28. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    29. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Tvede, Mich & Østerdal, Lars Peter, 2017. "Sharing the proceeds from a hierarchical venture," Games and Economic Behavior, Elsevier, vol. 102(C), pages 98-110.
    30. Pulido, Manuel A. & Sanchez-Soriano, Joaquin, 2006. "Characterization of the core in games with restricted cooperation," European Journal of Operational Research, Elsevier, vol. 175(2), pages 860-869, December.
    31. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    32. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
    33. Moulin, Herve & Thomson, William, 1988. "Can everyone benefit from growth? : Two difficulties," Journal of Mathematical Economics, Elsevier, vol. 17(4), pages 339-345, September.
    34. Sung, Shao-Chin & Dimitrov, Dinko, 2010. "Computational complexity in additive hedonic games," European Journal of Operational Research, Elsevier, vol. 203(3), pages 635-639, June.
    35. Martínez, Ricardo & Moreno-Ternero, Juan D., 2022. "Compensation and sacrifice in the probabilistic rationing of indivisible units," European Journal of Operational Research, Elsevier, vol. 302(2), pages 740-751.
    36. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    37. Gusev, Vasily V., 2021. "Nash-stable coalition partition and potential functions in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1180-1188.
    38. Moulin, Herve, 1992. "An Application of the Shapley Value to Fair Division with Money," Econometrica, Econometric Society, vol. 60(6), pages 1331-1349, November.
    39. Thomson, William, 2012. "On The Axiomatics Of Resource Allocation: Interpreting The Consistency Principle," Economics and Philosophy, Cambridge University Press, vol. 28(3), pages 385-421, November.
    40. Agustín G. Bonifacio & Elena Inarra & Pablo Neme, 2022. "Stable Decompositions of Coalition Formation Games," Working Papers 110, Red Nacional de Investigadores en Economía (RedNIE).
    41. William Thomson, 2023. "The Axiomatics of Economic Design, Vol. 1," Studies in Choice and Welfare, Springer, number 978-3-031-29398-6, June.
    42. Gudmundsson, Jens & Hougaard, Jens Leth & Platz, Trine Tornøe, 2023. "Decentralized task coordination," European Journal of Operational Research, Elsevier, vol. 304(2), pages 851-864.
    43. Chun, Youngsub & Thomson, William, 1988. "Monotonicity properties of bargaining solutions when applied to economics," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 11-27, February.
    44. Martin Gairing & Rahul Savani, 2019. "Computing Stable Outcomes in Symmetric Additively Separable Hedonic Games," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1101-1121, August.
    45. Daniel J. Seidmann & Eyal Winter, 1998. "A Theory of Gradual Coalition Formation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(4), pages 793-815.
    46. Marek Pycia, 2012. "Stability and Preference Alignment in Matching and Coalition Formation," Econometrica, Econometric Society, vol. 80(1), pages 323-362, January.
    47. Michel Breton & Ignacio Ortuño-Ortin & Shlomo Weber, 2008. "Gamson’s law and hedonic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(1), pages 57-67, January.
    48. William Thomson, 2023. "Complements to the Axiomatic Method in Economic Design," Studies in Choice and Welfare, in: The Axiomatics of Economic Design, Vol. 1, chapter 0, pages 269-285, Springer.
    49. Lensberg, Terje, 1987. "Stability and Collective Rationality," Econometrica, Econometric Society, vol. 55(4), pages 935-961, July.
    50. Moulin, Herve & Roemer, John, 1989. "Public Ownership of the External World and Private Ownership of Self," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 347-367, April.
    51. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
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