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.
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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