Abstract
We strategically separate different core outcomes. The natural counterparts of a core allocation in a strategic environment are the α-core, the β-core and the strong equilibrium, modified by assuming that utility is transferable in a strategic context as well. Given a core allocation ω of a convex transferable utility (TU) game \(v\), we associate a strategic coalition formation game with \( \left( {v, \omega } \right) \) in which ω survives, while most other core allocations are eliminated. If the TU game is strictly convex, the core allocations respected by the TU-α-core, the TU-β-core and the TU-strong equilibrium shrink to ω only in the canonical family of coalition formation games associated with \( \left( {v, \omega } \right) \). A mechanism, which strategically separates core outcomes from noncore outcomes for each convex TU game according to the TU-strong equilibrium notion is reported.
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Notes
Player 1 is the row player as usual, where the first components in each cell refer to his payoff at that outcome. Player 2 is the column player whose payoffs are represented by the second component in each cell.
This construction was also given by von Neumann and Morgenstern (1944).
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Acknowledgements
BIDEB-2211 Graduate Scholarship Program of the Scientific and Technological Research Council of Turkey (TUBİTAK) and Foundation for Economic Design are gratefully acknowledged for financial support to Y.D.
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Dede, Y., Koray, S. Every member of the core is as respectful as any other. Rev Econ Design 22, 55–65 (2018). https://doi.org/10.1007/s10058-018-0211-6
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DOI: https://doi.org/10.1007/s10058-018-0211-6