Abstract
Debreu and Scarf (Int Econ Rev 4:235–246, 1963) proved that for an exchange economy or a production economy with the same production set for all coalitions, under some standard assumptions, an Edgeworth equilibrium is a competitive equilibrium, and Florenzano (J Math Anal Appl 153:18–36, 1990) proved that for such an economy, any allocation in the fuzzy core is an Edgeworth equilibrium. These results are extended to coalition production economies where each coalition can have a different production set. In fact, we establish the coincidence of the fuzzy core, the set of Edgeworth equilibria, and the set of competitive equilibria in a coalition production economy under some standard assumptions. We then prove the existence of the fuzzy core in such a coalition production economy by using a fuzzy extension of Scarf’s core existence theorem, thereby establishing the existence of Edgeworth equilibria and competitive equilibria in such economies.
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Acknowledgments
The authors would like to thank the referees for their many helpful and inspiring suggestions and comments which resulted significant improvements to the paper. In particular, we thank one referee for one comment which made an important improvement in the presentation of the proof for Theorem 3.5 and the other referee for one comment which leads to Proposition 4.2 and the current more important version of Theorem 4.6 - the coincidence theorem of the fuzzy core, the set of Edgeworth equilibria, and the set of competitive equilibria of a coalition production economy \(\mathcal {E}\). We also thank the Science Foundation of Shaanxi Province, P. R. China (2011JM9011) for the support.
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Liu, J., Liu, X. Existence of Edgeworth and competitive equilibria and fuzzy cores in coalition production economies. Int J Game Theory 43, 975–990 (2014). https://doi.org/10.1007/s00182-014-0414-1
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DOI: https://doi.org/10.1007/s00182-014-0414-1