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The Myerson Value and Superfluous Supports in Union Stable Systems

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Abstract

In this paper, the set of feasible coalitions in a cooperative game is given by a union stable system. Well-known examples of such systems are communication situations and permission structures. Two games associated with a game on a union stable system are the restricted game (on the set of players in the game) and the conference game (on the set of supports of the system). We define two types of superfluous support property through these two games and provide new characterizations for the Myerson value. Finally, we analyze inheritance of properties between the restricted game and the conference game.

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Notes

  1. Although in the beginning of this section, we mentioned that we always take as player set N={1,…,n}, the definition of the conference game is the only occasion where we deviate from this. Note that the player set in a conference game is still derived from a structure on N.

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Acknowledgements

This research was finished while the first author was visiting Tinbergen Institute and VU University Amsterdam, under grant Ref. 24022011 of Seville University. Also, this visit was partially supported by Tinbergen Institute. Moreover, this work was presented in some conferences under financial support of the project ECO201017766.

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Authors and Affiliations

  1. Matemática Aplicada II, Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n, 41092, Sevilla, Spain

    E. Algaba & J. M. Bilbao

  2. Department of Econometrics, VU University and Tinbergen Institute, De Boelelaan 1105, 1081 HV, Amsterdam, The Netherlands

    R. van den Brink

  3. Matemática Aplicada II, Escuela Universitaria Politécnica, Virgen de África 7, 41011, Sevilla, Spain

    J. J. López

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  1. E. Algaba
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  2. J. M. Bilbao
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  3. R. van den Brink
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  4. J. J. López
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Correspondence to E. Algaba.

Additional information

Communicated by Irinel Chiril Dragan.

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Algaba, E., Bilbao, J.M., van den Brink, R. et al. The Myerson Value and Superfluous Supports in Union Stable Systems. J Optim Theory Appl 155, 650–668 (2012). https://doi.org/10.1007/s10957-012-0077-7

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