Urbinati, Niccolò (2018): A convexity result for the range of vector measures with applications to large economies.

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Abstract
On a Boolean algebra we consider the topology $u$ induced by a finitely additive measure $\mu$ with values in a locally convex space and formulate a condition on $u$ that is sufficient to guarantee the convexity and weak compactness of the range of $\mu$. This result à la Lyapunov extends those obtained in (Khan, Sagara 2013) to the finitely additive setting through a more direct and less involved proof. We will then give an economical interpretation of the topology $u$ in the framework of coalitional large economies to tackle the problem of measuring the bargaining power of coalitions when the commodity space is infinite dimensional and locally convex. We will show that our condition on $u$ plays the role of the "many more agents than commodities" condition introduced by Rustichini and Yannelis in (1991). As a consequence of the convexity theorem, we will obtain two straight generalizations of Schmeidler's and Vind's Theorems on the veto power of coalitions of arbitrary economic weight.
Item Type:  MPRA Paper 

Original Title:  A convexity result for the range of vector measures with applications to large economies 
English Title:  A convexity result for the range of vector measures with applications to large economies 
Language:  English 
Keywords:  Lyapunov's Theorem; finitely additive measures; correspondences; coalitional economies 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games D  Microeconomics > D5  General Equilibrium and Disequilibrium > D51  Exchange and Production Economies 
Item ID:  87185 
Depositing User:  Niccolò Urbinati 
Date Deposited:  07 Jun 2018 08:54 
Last Modified:  29 Sep 2019 11:54 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/87185 