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A linear proportional effort allocation rule

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  • Kamijo, Yoshio

Abstract

This paper proposes a new class of allocation rules in network games. Like the solution theory in cooperative games of how the Harsanyi dividend of each coalition is distributed among a set of players, this new class of allocation rules focuses on the distribution of the dividend of each network. The dividend of each network is allocated in proportion to some measure of each player's effort, which is called an effort function. With linearity of the allocation rules, an allocation rule is specified by the effort functions. These types of allocation rules are called linear proportional effort allocation rules. Two famous allocation rules, the Myerson value and the position value, belong to this class of allocation rules. In this study, we provide a unifying approach to define the two aforementioned values. Moreover, we provide an axiomatic analysis of this class of allocation rules, and axiomatize the Myerson value, the position value, and their non-symmetric generalizations in terms of effort functions. We propose a new allocation rule in network games that also belongs to this class of allocation rules.

Suggested Citation

  • Kamijo, Yoshio, 2009. "A linear proportional effort allocation rule," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 341-353, November.
  • Handle: RePEc:eee:matsoc:v:58:y:2009:i:3:p:341-353
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    References listed on IDEAS

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    1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
    2. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 27-39.
    3. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 87-110, February.
    4. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    5. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    6. 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.
    7. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 23-38.
    8. André Casajus, 2007. "The position value is the Myerson value, in a sense," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 47-55, September.
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    Cited by:

    1. repec:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1074-4 is not listed on IDEAS
    2. Borkotokey, Surajit & Sarangi, Sudipta, 2011. "Allocation rules for fixed and flexible networks: the role of players and their links," MPRA Paper 38340, University Library of Munich, Germany.
    3. Borkotokey, Surajit & Kumar, Rajnish & Sarangi, Sudipta, 2015. "A solution concept for network games: The role of multilateral interactions," European Journal of Operational Research, Elsevier, vol. 243(3), pages 912-920.

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