Abstract
We introduce a two-sided market situation with a central player. This player plays both the role of buyer and seller. From this situation we consider the corresponding TU-game and describe the core of the game in terms of the market data. We also study two point solutions: the nucleolus and the \(\tau \)-value. When we allow the central player to have multiple partners, the game is still balanced and each competitive equilibrium provides a core allocation.
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Notes
For technical reasons, we will consider, if necessary, that in case of only one seller we can assume a fictious seller with \(a_{2h}=0\), and similarly, a fictious second buyer with \(a_{h2}=0\) in case of only one buyer.
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Acknowledgements
We gratefully thank Marina Núñez and two anonymous referees for their suggestions, especially, the idea given by an anonymous referee to improve the characterization of the nucleolus of assignment games with a central player. The authors also acknowledge the support from the research grant ECO2017-86481-P (Ministerio de Economía y Competitividad).
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El Obadi, S., Miquel, S. Assignment Games with a Central Player. Group Decis Negot 28, 1129–1148 (2019). https://doi.org/10.1007/s10726-019-09638-1
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DOI: https://doi.org/10.1007/s10726-019-09638-1