Some equivalence results for a bargaining set in finite economies

Abstract

We present a bargaining set for finite economies using Aubin's () veto and show its coincidence with the set of Walrasian allocations, providing a discrete approach to the characterization of competitive equilibria obtained by Mas‐Colell () for continuum economies. We also study how the restriction on the formation of coalitions affects the bargaining set. In the last part of the work, using our equivalence result along with some known characterizations of Walrasian allocations, we state additional interpretations of the bargaining set.

Fairness and fuzzy coalitions

“…Actually from Theorem 1 of Graziano et al (2020) it follows that Corollary 3.5(1) can be extended to the bargaining set as defined by Hervés-Estévez and Moreno-García (2018a) (see also Hervés-Estévez and Moreno-García 2018b;Hervés-Beloso et al 2018) and Corollary 3.5(2) also to the bargaining set defined by Mas-Colell (1989) (see Liu and Zhang 2016 for the equivalence in coalition production economies).…”

Fairness and formation rules of coalitions

“…For example, Khan (1974) considers the core of a finite economy, Hervés‐Beloso et al (2000) and Evren and Hüsseinov (2008) study economies with infinite‐dimensional commodity space, Hervés‐Beloso et al (2005b) and Hervés‐Beloso et al (2014) examine economies with asymmetric information, Hervés‐Beloso et al (2005a) and Bhowmik and Cao (2012) combine asymmetric information and infinite‐dimensional commodity space, Gilles (2019) considers production economies, and Basile et al (2021) allow also the presence of collective goods. Shimomura (2022) and Hervés‐Estévez and Moreno‐García (2018) study, instead, how the restriction on the formation of coalitions affects the bargaining set defined as a weakening of the core. Okuda and Shitovitz (1985) analyze the core under inclusion/exclusion coalition formation rules, Bimonte and Graziano (2009) examine economies with asymmetric information, Basile and Graziano (2001) consider a coalitional approach, while Basile et al (2010) combine asymmetric information and coalitional approach.…”

Equivalence of Competitive Equilibria, Fuzzy Cores, and Fuzzy Bargaining Sets in Finite Production Economies

“…In 1979, Aubin [13] introduced the notion of fuzzy core (see also [14,15]) for an exchange economy by using fuzzy coalitions which allow agents to participate in a coalition with any level between 0 and 100 percentage, and proved that the fuzzy core and the set of competitive equilibrium allocations coincide in a finite exchange economy. Using Aubin's veto mechanism [16] through fuzzy coalitions, Herv és-Est évez and Moreno-Garc ía [17] and Liu [18] proved that the fuzzy (Aubin) bargaining set coincides with the set of competitive allocations in a finite economy with a finite-dimensional Euclidean commodity space under standard assumptions.…”