Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy

Mas-Colell (J Math Econ 18:129–139, 1989) proved that the bargaining set and the set of competitive allocations coincide in an exchange economy with a continuum of traders under some standard assumptions. We extend this result to continuum coalition production economies and prove that the bargaining set and the set of competitive allocations coincide in a coalition production economy with a continuum of traders under some standard assumptions. As a consequence, we obtain a coincidence theorem for the core and the set of competitive allocations in a coalition production economy which extends the well-known coincidence theorem by Aumann (Econometrica 32:39–50, 1964).

[1]  Benyamin Shitovitz,et al.  Oligopoly in Markets with a Continuum of Traders , 1973 .

[2]  T. Bewley.  Existence of equilibria in economies with infinitely many commodities , 1972 .

[3]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[4]  Herbert E. Scarf,et al.  A LIMIT THEOREM ON THE CORE OF AN ECONOMY , 1963, Classics in Game Theory.

[5]  W. Hildenbrand.  Existence of Equilibria for Economies with Production and a Measure Space of Consumers , 1970 .

[6]  R. Aumann.  INTEGRALS OF SET-VALUED FUNCTIONS , 1965 .

[7]  David Schmeidler,et al.  Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences , 1969 .

[8]  Jiuqiang Liu.  Existence of competitive equilibrium in coalition production economies with a continuum of agents , 2017, Int. J. Game Theory.

[9]  Tom Armstrong,et al.  The core-walras equivalence , 1984 .

[10]  R. Aumann.  Markets with a continuum of traders , 1964 .

[11]  Department of Economics University of Vienna on Core-walras Equivalence in Banach Spaces When , 2022 .

[12]  G. Debreu,et al.  Theory of Value , 1959 .

[13]  Finitely Additive Nonatomic Coalition Production Economies: Core-Walras Equivalence , 1993 .

[14]  On core-Walras equivalence in Banach lattices , 2005 .

[15]  Robert J. Aumann,et al.  EXISTENCE OF COMPETITIVE EQUILIBRIA IN MARKETS WITH A CONTINUUM OF TRADERS , 2020, Classics in Game Theory.

[16]  A. Mas-Colell.  An equivalence theorem for a bargaining set , 1989 .

[17]  Volker Boehm,et al.  The Core of an Economy with Production , 1974 .

[18]  Werner Hildenbrand,et al.  The Core of an Economy with a Measure Space of Economic Agents , 1968 .

[19]  Existence of equilibria in atomless production economies with price dependent preferences , 1979 .

[20]  Nicholas C. Yannelis,et al.  Equilibrium theory with asymmetric information and with infinitely many commodities , 2008, J. Econ. Theory.

[21]  Jean Jaskold Gabszewicz,et al.  An Equivalence Theorem for the Core of an Economy Whose Atoms Are Not 'Too' Big , 1971 .