Abstract
In this paper, we define bi-linear games as a generalization of the bimatrix games. In particular, we generalize concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space. For a special type of Z-transformation we observe relationship between the values of the linear and bi-linear games. Using this relationship, we prove some known classical results in the theory of linear complementarity problems for this type of Z-transformations.
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Acknowledgement
The authors like to thank the anonymous referee for pointing out a result due to Gowda and Ravindran (Theorem 6 in [6]) which improved the paper significantly.
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The first author thanks the University Grants Commission, India for the financial support through UGC — SRF (S.ID: 421898).
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Sengodan, G., Arumugasamy, C. Linear Complementarity Problems and Bi-Linear Games. Appl Math 65, 665–675 (2020). https://doi.org/10.21136/AM.2020.0371-19
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DOI: https://doi.org/10.21136/AM.2020.0371-19