Coalitional fairness with participation rates

Abstract

This paper investigates coalitional fairness in pure exchange economies\ud with asymmetric information. We study allocations of resources which are immune\ud from envy when comparisons take place between coalitions. The model allows negligible\ud and non-negligible traders, partially informed about the true state of nature at\ud the time of consumption, to exchange any number, possibly infinite, of commodities.\ud Our analysis is based on the Aubin approach to coalitions and cooperation. Namely,\ud on a notion of cooperation allowing traders to take part in one or more coalitions\ud simultaneously, employing only shares of their endowments (participation rates). We\ud introduce and study in detail the notion of coalition fairness with participation rates (or\ud Aubin c-fairness) and show that flexibility in cooperation permits to recover the failure\ud of fairness properties of equilibrium allocations. Our results provide applications\ud to several market outcomes (ex-post core, fine core, ex-post competitive equilibria,\ud rational expectations equilibria) and emphasize the consequences of the convexification\ud effect due to participation rates for models with large traders and infinitely many\ud commodities

Fairness and fuzzy coalitions

“…Similar considerations have been done by Basile et al (2018) for coalitional fair allocations and by Graziano et al (2020) for the bargaining set.…”

“…In order to prove the reverse inclusion F S F ⊆ W ei we need the following lemma, which can be viewed as an extension to mixed markets of Lemma 3.3 of Zhou (1992) (see also Thomson and Zhou 1993;Basile et al 2018 for infinite-dimensional separable commodity space).…”

“…The literature of fair division is huge and rich of various equity notions proposed in decades of research. This paper focuses on the notion of strict fairness due to Zhou (1992) which has been recently studied by Cato (2010), who proposed a local version of S F by imposing absence of envy only among neighbors (see also Donnini and Pesce 2021), by Basile et al (2018) who compared S F with a coalitional fairness notion in economies with infinitely many goods, by Donnini and Pesce (2020) who got the equivalence W ei = S F in mixed markets under stronger assumptions than those used to prove the Core-Walras equivalence theorem (Shitovitz 1973). In this paper, we keep the model of mixed markets but, weakening the notion of strict fairness, we avoid additional conditions on the space of agents as well as restrictions on the set of potentially envied agents.…”