Recently, we found the paper by John Dickhaut and Todd Kaplan that describes a program written in Wolfram Mathematica for finding Nash equilibria (Dickhaut and Kaplan, Economic and financial modeling with mathematica®, TELOS and Springer, New York, pp 148–166, 1993, ). (An introductory course on mathematical game theory, American Mathematical Society, XIV+324 pp, 2010, ), Sagaidac and Ungureanu (Operational research, CEP USM, Chişinău, 296 pp (in Romanian), 2004, ), Ungureanu (Set of nash equilibria in \(2\times 2\) mixed extended games, from the Wolfram demonstrations project, 2007, ), Stahl (A gentle introduction to game theory, American Mathematical Society, XII+176 pp, 1999, ), Barron (Game theory: an introduction, 2nd ed, Wiley, Hoboken, XVIII+555 pp, 2013, ), Gintis (Game theory evolving: a problem-centered introduction to modeling strategic interaction, 2nd ed, Princeton University Press, Princeton and Oxford, XVIII+390 pp, 2009, ). Vorob’ev (Foundations of game theory: noncooperative games, Nauka, Moscow (in Russian), 1984, Game theory: lectures for economists and systems scientists, Nauka, Moscow (in Russian), 1985, ), Gonzalez-Diaz et al. These types of games where considered earlier in a series of works, e.g. set-valued/multi-valued Nash equilibrium set function (Nash function) \(\) of two real spaces of two \(2\times 2\) matrices and in the quality of a Nash function image all possible sets of Nash equilibria in dyadic bimatrix mixed-strategy games. In contrast to other games, we obtain not only an algorithm, but a. As in the precedent chapters, the set of Nash equilibria in a particular game is determined as an intersection of graphs of optimal reaction mappings of the first and the second players. Dyadic two-person mixed strategy games form the simplest case for which we can determine straightforwardly Nash equilibrium sets.
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