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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.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 58 (2009)
Issue (Month): 3 (November)
Pages: 341-353

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Handle: RePEc:eee:matsoc:v:58:y:2009:i:3:p:341-353

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Web page: http://www.elsevier.com/locate/inca/505565

Related research

Keywords: Network games Linear proportional effort allocation rules Axiomatization Myerson value Position value;

References

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  1. Matthew O. Jackson & Asher Wolinsky, 1995. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer, vol. 21(1), pages 27-39.
  3. Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Working Papers 2003.51, Fondazione Eni Enrico Mattei.
  4. André Casajus, 2007. "The position value is the Myerson value, in a sense," International Journal of Game Theory, Springer, vol. 36(1), pages 47-55, September.
  5. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer, vol. 29(1), pages 23-38.
  6. René van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers 04-095/1, Tinbergen Institute.
  7. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154855, Tilburg University.
  8. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November.
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Cited by:
  1. 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.

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