Computation of Nash Equilibria of Two-Person Non-Cooperative Games with Maple

We develop a Maple code that computes the solutions of two-person non-cooperative games. When the bimatrix game of any two-player, two-strategy, including bimatrix games with symbolic entries, is inputted into our Maple package, the program outputs all the Nash equilibrium strategy pairs (pure and/or mixed) along their corresponding payoffs. When the bimatrix game of any two-player, m×n strategy game is inputted into our Maple package, the program outputs only the pure Nash equilibrium strategy pairs along their corresponding payoffs. The Theory of Games concerns the mathematics of decision making. It provides a general framework within which both cooperation and competition among independent agents may be modeled and gives powerful tools for analyzing these models. A game is said to be non-cooperative if each agent involved pursues his or her own interests which are partially conflicting with others'. Non-cooperative games are important tools which are extensively used in economics, social sciences, political science, computer science, biology, and in others fields. The main goal in game theory is the identification of potential Nash equilibria of a given game. The calculation of Nash Equilibria by hand is often tedious and time consuming even when the game is fairly small and may be impossible for large games. Because of these difficulties, calculations of Nash equilibria readily lend themselves to computer programming. Computation of Nash equilibria has been extensively studied and programs for finding Nash equilibria are available. However, all the existing methods and programs are numerical in nature and therefore cannot be used if the payoff matrices in a game contain entries that are parameters or symbolic values. However, in many applications of game theory, the bimatrix game contains entries which are parameters, hence the need to develop a new program. The following examples illustrate bimatrix games with entries that are parameters.