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Values For Games On The Cycles Of A Digraph

Author

Listed:
  • WILLIAM OLVERA-LOPEZ

    (Centro de Investigación en Matemáticas A.C., Jalisco S/N, Valenciana. Guanajuato, México. A.P. 403, México)

  • FRANCISCO SANCHEZ-SANCHEZ

    (Centro de Investigación en Matemáticas A.C., Jalisco S/N, Valenciana. Guanajuato, México. A.P. 403, México)

Abstract

In this paper we introduce a new class of cooperative games. We define a characteristic function over the cycles of a digraph. We present a mathematical model for this situation and an axiomatic characterization of a solution for this class of cooperative games. This is introduced as a method to measure the importance of the nodes in a digraph, and can be related with the Shapley value of a game in characteristic function form. Also, we extend the modeling by applying coalitional structures for the nodes andr-efficient solutions, where the allocation amount is a real numberr, showing axiomatic solutions in both cases.

Suggested Citation

  • William Olvera-Lopez & Francisco Sanchez-Sanchez, 2012. "Values For Games On The Cycles Of A Digraph," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 1-18.
    • Handle: RePEc:wsi:igtrxx:v:14:y:2012:i:02:n:s0219198912500089
    DOI: 10.1142/S0219198912500089
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    More about this item

    Keywords

    Digraphs; cooperative games; allocation rules; 05C57; 91A12; 91A43;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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