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Harsanyi power solutions for graph-restricted games

  • René Brink

    ()

  • Gerard Laan

    ()

  • Vitaly Pruzhansky

    ()

This discussion paper resulted in a publication in the 'International Journal of Game Theory', 40, 87-110. A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff distributions (possibly empty or consisting of a unique element) to every TU-game. Harsanyi solutions are solutions that are based on distributing dividends. In this paper we consider games with limited communication structure in which the edges or links of an undirected graph on the set of players represent binary communication links between the players such that players can cooperate if and only if they are connected. For such games we discuss Harsanyi solutions whose dividend shares are based on power measures for nodes in corresponding communication graphs. Special attention is given to the Harsanyi degree solution which equals the Shapley value on the class of complete graph games (i.e. the class of TU-games) and equals the position value on the class of cycle-free graph games. Another example is the Harsanyi power solution that is based on the equal power measure, which turns out to be the Myerson value. Various applications of our results are provided.

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File URL: http://hdl.handle.net/10.1007/s00182-009-0220-3
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Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 40 (2011)
Issue (Month): 1 (February)
Pages: 87-110

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Handle: RePEc:spr:jogath:v:40:y:2011:i:1:p:87-110
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  1. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer, vol. 24(3), pages 439-454, 06.
  2. Daniel Gómez & Enrique Gonz{\'a}lez-Arangüena & Conrado Manuel & Guillermo Owen & Monica Del Pozo, 2004. "A Unified Approach To The Myerson Value And The Position Value," Theory and Decision, Springer, vol. 56(2_2), pages 63-76, 02.
  3. Daniel Gómez & Enrique Gonz{\’a}lez-Arangüena & Conrado Manuel & Guillermo Owen & Monica Del Pozo, 2004. "A Unified Approach To The Myerson Value And The Position Value," Theory and Decision, Springer, vol. 56(1), pages 63-76, 04.
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  8. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November.
  9. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
  10. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
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