Mixed strategy nash equilibrium 2x3 games

Nash equilibria sets in mixed extended 2x3 games Valeriu Ungureanu. A short summary of this paper. Download Download PDF. Translate PDF. Computer Science Journal of Moldova, vol. Keywords and phrases: Noncooperative game; Nash equi- librium, Nash equilibria set, best response graph.

This paper may be considered a continuation of [5] and it has to illustrate the practical opportunity of a mentioned characteristic. Elements of X are named outcomes of the game situations or strategy profiles. Ungureanu, A. There are diverse alternative formulations of a Nash equilibrium [1]: as a fixed point of the best response correspondence, as a fixed point of a function, as a solution of a non-linear complementarity problem, as a solution of a stationary point problem, as a minimum of a function on a polytope, as a semi-algebraic set.

We study the Nash equilibria set as an intersection of best response graphs [4, 5], i. They may be Pareto ranked. Therefore Nash equilibrium may domi- nate or it may be dominated.

There are also different other criteria for Nash equilibria distinguishing such as perfect equilibria, proper equilib- ria, sequential equilibria, stable sets etc. Evidently, a method for all Nash equilibria determination is useful and required.

Other theoretical and practical factors that argue for NE set determination exist [1]. This paper as the continuation of [5] investigates the problems of NE set construction in the games that permit simple graphic illustrations and that elucidate the usefulness of the interpretation of NE as an intersection of best response graphs [4, 5]. This game is reduced to the game on the unit prism. From this the truth of the proposition results.

Botnari Proposition 2. Thus, the NE set contains either only one vertex of a unit prism 4 as an intersection of one facet Gr1 with one edge Gr2 or only one edge of a unit prism 4 as an intersection of one facet Gr1 with one edge Gr2. Normally I would just solve for q but I'm not sure how what to do with two variables.

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