Bhowmik, Anuj (2014): Core and Coalitional Fairness: The Case of Information Sharing Rule.
PDF
MPRA_paper_56644.pdf Download (404kB) 
Abstract
We investigate two of the most extensively studied cooperative notions in a pure exchange economy with asymmetric information. One of them is the core and the other is known as coalitional fairness. The set of agents is modelled by a mixed market consisting of some large agents and an ocean of small agents; and the commodity space is an ordered Banach space whose positive cone has an interior point. The information system in our framework is the one introduced by Allen in [1]. Thus, the same agent can have common, private or pooled information when she becomes member of different coalitions. It is shown that the main results in Grodal [20], Schmeidler [26] and Vind [31] can be established when the economy consists of a continuum of small agents. We also focus on the information mechanism based on size of coalitions introduced in [18] and obtain a result similar to the main result in [18]. Finally, we examine the concept of coalitional fairness proposed in [21]. We prove that the core is contained in the set of coalitionally fair allocations under some assumptions. This result provides extensions of Theorem 2 in [21] to an economy with asymmetric information as well as a deterministic economy with infinitely many commodities. Although we consider a general commodity space, all our results were so far unsolved to the case of information sharing rule with finitely many commodities.
Item Type:  MPRA Paper 

Original Title:  Core and Coalitional Fairness: The Case of Information Sharing Rule 
English Title:  Core and Coalitional Fairness: The Case of Information Sharing Rule 
Language:  English 
Keywords:  Asymmetric information economy; coalitional fairness; core; information sharing rule. 
Subjects:  D  Microeconomics > D5  General Equilibrium and Disequilibrium > D51  Exchange and Production Economies D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D82  Asymmetric and Private Information ; Mechanism Design 
Item ID:  57372 
Depositing User:  Dr. Anuj Bhowmik 
Date Deposited:  17 Jul 2014 13:09 
Last Modified:  20 Oct 2019 04:33 
References:  [1] B. Allen, Market games with asymmetric information: the core, Econ. Theory {\bf 29} (2006), 465487. [2] L. Angeloni, V.F. MartinsdaRocha, Large economies with differential information and without disposal, Econ. Theory {\bf 38} (2009), 263286. [3] K. J. Arrow, G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica {\bf 22} (1954), 265290. [4] R.J. Aumann, Markets with a continuum of traders, Econometrica {\bf 32} (1964), 3950. [5] A. Bhowmik, J. Cao, Blocking efficiency in an economy with asymmetric information, J Math Econ {\bf 48} (2012), 396403. [6] A. Bhowmik, J. Cao, Robust efficiency in mixed economies with asymmetric information, J Math Econ {\bf 49} (2013), 4957. [7] A. Bhowmik, J. Cao, On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces, Econ. Theory, {\bf 53} (2013), 537560. [8] A. Bhowmik, Edgeworth's conjecture under differential information, submitted 2013. [9] G. Debreu, H. Scarf, A limit theorem on the core of an economy, Int Econ Rev {\bf 4} (1963), 235246. [10] C. donnini, M.G. Graziano, M. Pesce, Coalitional fairness in interim differential information economies, J. Econ. {\bf 111} (2014), 5568. [11] E. Einy, D. Moreno, B. Shitovitz, On the core of an economy with differential information, J Econ Theory {\bf 94} (2000), 262270. [12] E. Einy, D. Moreno, B. Shitovitz, Competitive and core allocations in large economies with differentiated information, Econ Theory {\bf 18} (2001), 321332. [13] \"{O}. Evren, F. H\"{u}sseinov, Theorems on the core of an economy with infinitely many commodities and consumers, J. Math. Econ. {\bf 44} (2008), 11801196. [14] D. Foley, Resource allocation and the public sector, Yale Econ Essays {\bf 7} (1967), 4598. [15] C. Herv\'{e}sBeloso, E. MorenoGarc\'{i}a, C. N\'{u}\~{n}ezSanz, M.R. P\'{a}scoa, Blocking efficiency of small coalitions in myopic economies, J. Econ. Theory {\bf 93} (2000), 7286. [16] C. Herv\'{e}sBeloso, E. MorenoGarc\'{i}a, N.C. Yannelis, An equivalence theorem for a differential information economy, J. Math. Econ. {\bf 41} (2005), 844856. [17] C. Herv\'{e}sBeloso, E. MorenoGarc\'{i}a, N.C. Yannelis, Characterization and incentive compatibility of Walrasian expectations equilibrium in infinite dimensional commodity spaces, Econ. Theory {\bf 26} (2005), 361381. [18] C. Herv\'{e}sBeloso, C. Meo, E. MorenoGarc\'{i}a, Information and size of coalitions, Econ Thoery (2014), DOI 10. 1007/s0019901307702 [19] M.G. Graziano, M. Pesce, A Note on the Private Core and Coalitional Fairness under Asymmetric Information, Mediterr. J. Math. {\bf 7} (2010), 573–601. [20] B. Grodal, A second remark on the core of an atomless economy, Econometrica {\bf 40} (1972), 581583. [21] J. JaskoldGabszewicz, Coalitional fairness of allocations in pure exchange economies, Econometrica {\bf 43} (1975), 661668. [22] L. Koutsougers, N.C. Yannelis, Incentive compatibility and information superiority of the core of an economy with differental information, Econ. Theory {\bf 3} (1993), 195216. [23] L. W. McKenzie, On the existence of general equilibrium for a competitive market, Econometrica {\bf 27} (1959), 5471. [24] C. N\'{u}\~{n}ez, El teorema de Liapunov en el mecanismo del veto, Revista de la Real Academia de Ciencias Exactas, F\'{i}sicas y Naturales, de Madrid, Tomo LXXXVII (1993), Cuaderno SegundoTercero. [25] O. Ore, Theory of equivalncece relations, Duke Math. J. {\bf 9} (1942), 573626. [26] D. Schmeidler, A remark on the core of an atomless economy, Econometrica {\bf 40} (1972), 579580. [27] D. Schmeidler, K. Vind, Fair Net Trades, Econometrica {\bf 40} (1972), 637642. [28] B. Shitovitz, Oligopoly in markets with a continuum of traders, Econometrica {\bf 41} (1973), 467501. [29] B. Shitovitz, Coalitional fair allocations in smooth mixed markets with an atomless sector, Math. Social Sci. {\bf 25} (1992), 2740. [30] H. Varian, Equity, envy and efficiency, J. Econ. Theory {\bf 9} (1974), 6391. [31] K. Vind, A third remark on the core of an atomless economy, Econometrica {\bf 40} (1972), 585586. [32] R. Wilson, Information, efficiency, and the core of an economy, Econometrica {\bf 46} (1978), 807816. [33] N.C. Yannelis, The core of an economy with differential information, Econ. Theory {\bf 1} (1991), 183197. [34] L. Zhou, Strictly fair allocations in large excahnge economies, J. Econ. Theory {\bf 57} (1992), 158175. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/57372 
Available Versions of this Item

Core and Coalitional Fairness: The Case of Information Sharing Rule. (deposited 18 Jun 2014 00:14)
 Core and Coalitional Fairness: The Case of Information Sharing Rule. (deposited 17 Jul 2014 13:09) [Currently Displayed]