Abstract
In this paper we propose a concept of coalitional fair allocation in order to solve the tension that may exist between efficiency and envy-freeness when agents are asymmetrically informed and the equity of allocations is evaluated at the interim stage.
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Notes
This assumption implies that the following correspondence has measurable graph: \(\Pi : T\rightarrow 2^\mathcal{F}\) defined by \(\Pi (t)=\Pi _ t\). It means that the set \(G_{\Pi }=\{(t, \mathcal{E}): \mathcal{E}\in \Pi _ t\}\) belongs to the product \(\sigma \)-algebras \(\mathcal{T}\otimes \mathcal{B}(2^\mathcal{F})\), where \(\mathcal{B}\) denotes the Borel \(\sigma \)-algebra.
See Graziano and Pesce (2012) for an analysis on coalitional fairness notion in differential information economies in which agents receive no signal at the time of contracting.
Differently from the perfect information notions, we will explicitly require Pareto efficiency due to the free disposal condition imposed on allocations.
It is just needed to put for all \(\omega \), the envious coalition \(S_1(\omega )\) equal to the whole set of agents \(T\) and the other coalition \(S_2(\omega )\) equal to the empty set.
Since the measure space of agents is assumed to be finite and complete, the measurability of the projection \(Proj_{T}S^*\) for each measurable subset \(S^ *\) of \(T^ *\) follows by the Projection Theorem (see Theorem 14.84 in Aliprantis and Border 2006).
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Acknowledgments
We would like to thank A. Basile for valuable comments.
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An earlier version of this paper circulated with the title “Fairness properties of constrained market equilibria” as CSEF working paper http://www.csef.it/WP/wp245.pdf.
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Donnini, C., Graziano, M.G. & Pesce, M. Coalitional fairness in interim differential information economies. J Econ 111, 55–68 (2014). https://doi.org/10.1007/s00712-012-0322-4
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DOI: https://doi.org/10.1007/s00712-012-0322-4