Abstract
Let (N, v) be a cooperative game with transferable utility and \(F\subseteq 2^N\) an arbitrary set system, where F represents the set of feasible coalitions S whose worths v(S) are known. We introduce a game \((N,v_F)\) as follows. If \(S\in F\), then \(v_F(S)=v(S)\) and otherwise \(v_F(S)\) is defined such that S has zero Harsanyi dividend. By taking different F, this model produces some well-known games directly or indirectly, such as hypergraph games. We characterize the Shapley value of \((N,v_F)\) on different domains similarly to that for the Myerson value.
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Notes
To coincide with the system game \(v^F\) defined in (5), here we write the hypergraph game as \(v^{\overline{H}}\) instead of \(v^H\) in the literature, where \(\overline{H}\) is the set of connected sets in H.
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Acknowledgements
We are grateful to D. Talman for inspiring discussions, and the Editor-in-Chief S. Zamir, the Associate Editor and two referees for invaluable comments and suggestions that improve the results and presentations substantially.
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This research was supported by NSFC (No. 11971298)
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Li, D.L., Shan, E. Cooperative games with partial information. Int J Game Theory 50, 297–309 (2021). https://doi.org/10.1007/s00182-021-00759-z
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DOI: https://doi.org/10.1007/s00182-021-00759-z