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Information collecting situations and bi-monotonic allocation schemes

Author

Listed:
  • Rodica Brânzei
  • Stef Tijs
  • Judith Timmer

Abstract

This paper studies information collecting (IC) situations with the help of cooperative game theory. Relations are established between IC situations and IC games on one hand and information sharing (IS) situations and IS games on the other hand. Further, it is shown that IC games are convex combinations of so-called local games. Properties such as k-convexity and k-concavity are possessed by an IC game if all related local games have the respective properties. Special attention is paid to the classes of k-symmetric IC games and k-concave IC games. This last class turns out to consist of total big boss games. For the class of total big boss games a new solution concept is introduced: bi-monotonic allocation schemes. This solution takes the power of the big boss into account. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Rodica Brânzei & Stef Tijs & Judith Timmer, 2001. "Information collecting situations and bi-monotonic allocation schemes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 303-313, December.
    • Handle: RePEc:spr:mathme:v:54:y:2001:i:2:p:303-313
    DOI: 10.1007/s001860100156
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    Citations

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    Cited by:

    1. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Convex Games Versus Clan Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 363-372.
    2. Alparslan Gök, S.Z. & Özcan, İ., 2023. "On big boss fuzzy interval games," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1040-1046.
    3. Tijs, S.H. & Moretti, S. & Brânzei, R. & Norde, H.W., 2005. "The Bird Core for Minimum Cost Spanning Tree problems Revisited : Monotonicity and Additivity Aspects," Other publications TiSEM 530f2c60-024d-4f3e-b724-1, Tilburg University, School of Economics and Management.
    4. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2011. "Convex games, clan games, and their marginal games," Center for Mathematical Economics Working Papers 368, Center for Mathematical Economics, Bielefeld University.
    5. Tijs, S.H. & Moretti, S. & Brânzei, R. & Norde, H.W., 2005. "The Bird Core for Minimum Cost Spanning Tree problems Revisited : Monotonicity and Additivity Aspects," Discussion Paper 2005-3, Tilburg University, Center for Economic Research.
    6. Brânzei, R. & Fragnelli, V. & Meca, A. & Tijs, S.H., 2006. "Two Classes of Cooperative Games Related to One-Object Auction Situations," Discussion Paper 2006-25, Tilburg University, Center for Economic Research.
    7. Tijs, S.H. & Brânzei, R. & Muto, S. & Ishihara, S. & Fukuda, E., 2002. "Fuzzy Clan Games and Bi-monotonic Allocation Rules," Discussion Paper 2002-115, Tilburg University, Center for Economic Research.
    8. Brânzei, R. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2007. "Multi-Choice Total Clan Games : Characterizations and Solution Concepts," Other publications TiSEM 31aee267-f432-46c8-b078-1, Tilburg University, School of Economics and Management.
    9. R. Branzei & N. Llorca & J. Sánchez-Soriano & S. Tijs, 2009. "Multi-choice clan games and their core," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 123-138, July.
    10. Brânzei, R. & Solymosi, T. & Tijs, S.H., 2003. "Type Monotonic Allocation Schemes for Multi-Glove Games," Discussion Paper 2003-34, Tilburg University, Center for Economic Research.
    11. Tijs, S.H. & Brânzei, R. & Muto, S. & Ishihara, S. & Fukuda, E., 2002. "Fuzzy Clan Games and Bi-monotonic Allocation Rules," Other publications TiSEM b5200e92-83d8-4fd9-b7f2-9, Tilburg University, School of Economics and Management.
    12. Brânzei, R. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2007. "Multi-Choice Total Clan Games : Characterizations and Solution Concepts," Discussion Paper 2007-77, Tilburg University, Center for Economic Research.

    More about this item

    Keywords

    JEL Classification Number: C71; D89.; Key words: cooperative games; information collecting; big boss games; bi-monotonic allocation scheme;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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