Existence of competitive equilibrium in coalition production economies with a continuum of agents

Aumann (Econometrica 34: 1–17, 1966) established the existence of competitive equilibria in exchange economies with a continuum of traders. This result has been extended to special production economies under the condition that the production sets are countably additive or superadditive in the literature. In this paper, we extend Aumann’s result to coalition production economies with a continuum of traders in which each coalition can have a different production set and the production sets need not to be additive or superadditive. Our new existence theorem for competitive equilibrium implies the classical result by Hildenbrand (Econometrica 38: 608–623, 1970), and implies those by Sondermann (J Econ Theory 8: 259–291, 1974) and Greenberg et al. (J Math Econ 6: 31–41, 1979) under the assumption that the production sets are convex.