Geodesic
Bimatrix games have a quasi-strict equilibrium: an alternative proof through a heuristic approach
The Teaching of Mathematics, XXI (2018) no. 2, p. 97

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We present an alternative proof for the existence of at least one quasi-strict equilibrium in every bimatrix game. While Norde [Bimatrix games have quasi-strict equilibria. Math Prog, {85}, 35-49] uses Brouwer's fixed point theorem, we employ Kakutani's fixed point theorem for multivalued maps, and make our proof shorter, thus teachable in a couple of lecture talks. Besides our approach admits of natural economic interpretations of some technicalities used in the proof. We also explain how we get to our method of proof. In addition, it is remarked that it is possible to adopt a field more general than that of real numbers.
Classification : 97M40, 91A05, 91B62 M45
Keywords: bimatrix game, Kakutani fixed point theorem, multivalued map, quasi-strict equilibrium. 
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     title = {Bimatrix games have a quasi-strict equilibrium: an alternative proof through a heuristic approach},
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Takao Fujimoto; N. G. A. Karunathilake; Ravindra R. Ranade. Bimatrix games have a quasi-strict equilibrium: an alternative proof through a heuristic approach. The Teaching of Mathematics, XXI (2018) no. 2, p. 97 . http://geodesic.mathdoc.fr/item/TM2_2018_XXI_2_a3/