Summary
A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally implements it. Our main theorem proves that a social choice set is coalitionally implementable if and only if it is interim individually rational, interim efficient, coalitional Bayesian incentive compatible, and satisfies a coalitional Bayesian monotonicity condition as well as a closure condition. As an application of our main result, we show that the private core and the private Shapley value of an economy with differential information are coalitionally implementable.
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We wish to thank the referees for several useful comments. Special thanks to D. Glycopantis for pointing out a calculation error in Example 5.1.
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Hahn, G., Yannelis, N.C. (2005). Coalitional Bayesian Nash implementation in differential information economies. In: Glycopantis, D., Yannelis, N.C. (eds) Differential Information Economies. Studies in Economic Theory, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26979-7_30
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DOI: https://doi.org/10.1007/3-540-26979-7_30
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