Computing all the Nash equilibria of a non-cooperative bimatrix game by hand is cumbersome, if not impossible. For this reason, the development of computer programs to solve bimatrix games has become an integral part of the study of game theory. In this paper we present a Maple package composed of two procedures, nashpm and payoff. When the user inputs an 𝑚 × 𝑛 bimatrix with real entries into nashpm, all the mixed and pure Nash equilibria of the game are outputted. When the user inputs the Nash equilibria solutions into the payoff procedure, the corresponding expected payoffs for each player are outputted. Our research extends a paper by Wang, Ahmed, and Gutierrez [1] which addressed the need for a computer program to calculate Nash equilibria of games with symbolic entries as well as numerical entries. This previous code only computed mixed strategy Nash equilibria for 2 × 2 bimatrix games, but the package presented here computes mixed strategy Nash equilibria for 𝑚 × 𝑛 bimatrix games. Additionally, our package can calculate mixed and pure strategy Nash equilibria of bimatrix games with symbolic entries.

Faculty Mentor: Dr. Aden Ahmed

Department of Mathematics