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Multi-attribute bi-matrix games

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  • Lahiri, Somdeb

Abstract

We introduce multi-attribute bi-matrix games and show that a strategy profile is an equilibrium strategy profile with respect to a preference relation satisfying additivity with respect to the zero vector for an arbitrary finite set of such games having the same number of attributes if and only if it solves a bi-linear programming problem and the value of the objective function at this solution is zero. An immediate consequence of this result, is that if the outcome matrix for the row player is a convex combination of its outcome matrices in the finite collection and the outcome matrix for the column player is a (possibly different) convex combination of its outcome matrices in the finite collection, then a strategy profile is an equilibrium strategy profile for the game associated with pair of matrices if and only if it satisfies the same two conditions.

Suggested Citation

  • Lahiri, Somdeb, 2026. "Multi-attribute bi-matrix games," MPRA Paper 129920, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:129920
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    File URL: https://mpra.ub.uni-muenchen.de/129920/14/MPRA_paper_129920.pdf
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    References listed on IDEAS

    as
    1. Ajay Kumar Bhurjee, 2016. "Existence of Equilibrium Points for Bimatrix Game with Interval Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-13, March.
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      JEL classification:

      • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
      • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
      • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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