Efficient extensions of the Myerson value
We study values for transferable utility games enriched by a communication graph (CO-games) where the graph does not necessarily affect the productivity but can influence the way the players distribute the worth generated by the grand coalition. Thus, we can envisage values that are efficient instead of values that are component efficient. For CO-games with connected graphs, efficiency and component efficiency coincide. In particular, the Myerson value (Myerson in Math Oper Res 2:22–229, 1977) is efficient for such games. Moreover, fairness is characteristic of the Myerson value. We identify the value that is efficient for all CO-games, coincides with the Myerson value for CO-games with connected graphs, and satisfies fairness.
Mathematics Subject Classification91A12
JEL ClassificationC71 D60
We are grateful to René van den Brink for valuable comments on this article. Financial support for Frank Huettner from the Deutsche Forschungsgemeinschaft (DFG) Grant HU 2205/1-1 is gratefully acknowledged. Moreover, financial support from research programs “DynaMITE: Dynamic Matching and Interactions: Theory and Experiments”, contract ANR-13-BSHS1-0010, and MODMAD is gratefully acknowledged.
- Casajus A (2007) An efficient value for TU games with a cooperation structure. Working paper, Universität Leipzig, GermanyGoogle Scholar
- Shapley LS (1953) A value for \(n\)-person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games, vol II. Princeton University Press, Princeton, pp 307–317Google Scholar
- van den Nouweland A (1993) Games and graphs in economic situations. Ph.D. thesis, Tilburg University, The NetherlandsGoogle Scholar