A note on bargaining sets in atomless economies

Maria Gabriella Graziano; Marialaura Pesce; Niccoló Urbinati

doi:10.3934/jdg.2024020

Article Contents

2025, Volume 12, Issue 4: 343-358. Doi: 10.3934/jdg.2024020

This issue Previous Article Next Article The veto power of the grand coalition in economies with consumption externalities

A note on bargaining sets in atomless economies

1.
Università di Napoli Federico Ⅱ, Dipartimento di Scienze Economiche e Statistiche, Italy
2.
Centre for Studies in Economics and Finance (CSEF), Italy

^*Corresponding author: Marialaura Pesce
^*Corresponding author: Marialaura Pesce

Dedicated to Professor Carlos Hervés-Beloso on the occasion of his 70th birthday

Received: July 2024

Early access: September 9, 2024

Published online: September 9, 2024

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Abstract

We consider an atomless exchange economy with a finite number of commodities. We introduce a new notion of bargaining set and show that it characterizes competitive allocations and, at the same time, it is robust to restrictions on the sizes of objecting and counterobjecting coalitions. Both results do not hold simultaneously for the bargaining sets defined by [18] and [23] for which we provide some new remarks.

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Mathematics Subject Classification: 91A40, 91B24, 91B50.

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References

[1]	R. J. Aumann, Markets with a continuum of traders, Econometrica, 32 (1964), 39-50. doi: 10.2307/1913732.
[2]	R. J. Aumann, Existence of competitive equilibria in markets with a continuum of traders, Econometrica, 34 (1966), 1-17. doi: 10.2307/1909854.
[3]	R. J. Aumann and M. Maschler, The bargaining set for cooperative games, Annals of Mathematics Studies, ed. by M. Dresher, L.S. Shapley and A.W. Tucker, Princeton University Press, Princeton, New Jersey, 52 (2015), 159-166.
[4]	B. Dutta, D. Ray, K. Sengupta and R. Vohra, A consistent bargaining set, Journal of Economic Theory, 49 (1989), 93-112. doi: 10.1016/0022-0531(89)90069-0.
[5]	J. García-Cutrín and C. Hervés-Beloso, A discrete approach to continuum economies, Economic Theory, 3 (1993), 577-583. doi: 10.1007/BF01209704.
[6]	M. G. Graziano, M. Pesce and N. Urbinati, Generalized coalitions and bargaining sets, Journal of Mathematical Economics, 91 (2020), 80-89. doi: 10.1016/j.jmateco.2020.08.008.
[7]	M. G. Graziano, M. Pesce and N. Urbinati, The equitable bargaining set, CSEF Working Paper #676, University of Naples Frederico Ⅱ, Naples, Italy, 2023.
[8]	J. R. Green, On the inequitable nature of core allocations, Journal of Economic Theory, 4 (1972), 132-143. doi: 10.1016/0022-0531(72)90144-5.
[9]	B. Grodal, A second remark on the core of an atomless economy, Econometrica, 40 (1972), 581-583. doi: 10.2307/1913187.
[10]	C. Hara, Bargaining set and anonymous core without the monotonicity assumption, Journal of Mathematical Economics, 41 (2005), 545-556. doi: 10.1016/j.jmateco.2004.12.001.
[11]	C. Hervés-Beloso, J. Hervés-Estévez and E. Moreno-García, Bargaining sets in finite economies, Journal of Mathematical Economics, 74 (2018), 93-98. doi: 10.1016/j.jmateco.2017.11.008.
[12]	C. Hervés-Beloso, C. Meo and E. Moreno-García, Information and size of coalitions, Economic Theory, 55 (2014), 545-563. doi: 10.1007/s00199-013-0770-2.
[13]	C. Hervés-Beloso and E. Moreno-García, Competitive equilibria and the grand coalition, Journal of Mathematical Economics, 44 (2008), 697-706. doi: 10.1016/j.jmateco.2006.11.002.
[14]	C. Hervés-Beloso, E. Moreno-García, C. Núñez and M. R. Pascoa, Blocking efficacy of small coalitions in myopic economies, Journal of Economic Theory, 93 (2000), 72-86. doi: 10.1006/jeth.2000.2647.
[15]	C. Hervés-Beloso, E. Moreno-García and N. C. Yannelis, Characterization and incentive compatibility of Walrasian expectations equilibrium in infinite dimensional commodity spaces, Economic Theory, 26 (2005), 361-381. doi: 10.1007/s00199-004-0497-1.
[16]	C. Hervés-Beloso, E. Moreno-García and N. C. Yannelis, An equivalence theorem for a differential information economy, Journal of Mathematical Economics, 41 (2005), 844-856. doi: 10.1016/j.jmateco.2004.01.004.
[17]	J. Hervés-Estévez and E. Moreno-García, On restricted bargaining sets, International Journal of Game Theory, 44 (2015), 631-645. doi: 10.1007/s00182-014-0447-5.
[18]	A. Mas-Colell, An equivalence theorem for a bargaining set, Journal of Mathematical Economics, 18 (1989), 129-139. doi: 10.1016/0304-4068(89)90017-7.
[19]	U. Schjodt and B. Sloth, Bargaining sets with small coalitions, International Journal of Game Theory, 23 (1994), 49-55. doi: 10.1007/BF01242846.
[20]	D. Schmeidler, A remark on the core of an atomless economy, Econometrica, 40 (1972), 579-580. doi: 10.2307/1913186.
[21]	K.-I. Shimomura, The bargaining set and coalition formation, International Journal of Economic Theory, 18 (2022), 16-37. doi: 10.1111/ijet.12320.
[22]	K. Vind, A third remark on the core of an atomless economy, Econometrica, 40 (1972), 585-586. doi: 10.2307/1913188.
[23]	K. Vind, Two characterizations of bargaining sets, Journal of Mathematical Economics, 21 (1992), 89-97. doi: 10.1016/0304-4068(92)90023-Z.
[24]	A. Yamazaki, Bargaining sets in continuum economies, in Nonlinear and Convex Analysis in Economic Theory, (1995), 289-299, Springer. doi: 10.1007/978-3-642-48719-4_24.
[25]	L. Zhou, A new bargaining set of an N-person game and endogenous coalition formation, Games and Economic Behavior, 6 (1994), 512-526. doi: 10.1006/game.1994.1030.