Bargaining sets in finite economies

Abstract

Abstract. We define a bargaining set for finite economies using Aubin's veto mechanism and show its coincidence with the set of Walrasian allocations.Then, we rewrite our notion in terms of replicated economies showing that, in contrast with Anderson, Trockel and Zhou's (1997) non-convergence result, this Edgeworth bargaining set shrinks to the set of Walrasian allocations.JEL Classification: D51, D11, D00.

Bargaining-Equilibrium Equivalence

“…in the specific case where agents participate in blocking coalitions with rational participation rates, they show that one can obtain the veto power when the finite economy is enlarged via replicas. Later, Hervés-Beloso et al [15] and Liu [18] extend the results of Hervés-Estévez and Moreno-García [17] to the case of a finite production economy and to the case of a finite coalitional production economy respectively. Liu and Zhang [19] provided a characterization of the competitive equilibrium allocations of a continuum economy with production in the spirit of Mas-Colell [22] and established that the bargaining sets for such economies are equivalent to the set of competitive allocation allocations.…”

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).…”

“…This policy is also widespread in the literature. See, among others, Florenzano (1990), Noguchi (2000), Liu and Liu (2014), Pesce (2014) and Bhowmik and Graziano (2015) for the equivalence Walras-Aubin-Core in different frameworks; Hervés-Estévez and Moreno-García (2015), Hervés-Beloso et al (2018) and Graziano et al (2020) for the link between W ei and the bargaining set, and Yang et al (2011) between the bargaining set and the Aubin-core. The paper is organized as follows.…”