A program to find all pure Nash equilibria in games with n-players and m-strategies: the Nash Equilibria Finder – NEFinder

Abstract

Nash equilibrium is an important concept for studying human behavior in group decision making process. Given the complexity of finding Nash equilibria, computational tools are necessary to find them. Several programs were developed for this task. However, available programs are either not comprehensive or might be of difficult installation and handling, creating a “barrier of entry” to non-specialists. The aims of this research are twofold: (i) firstly, it was to identify and to discuss about the available programs for finding Nash equilibria; and (ii) secondly, based on the theoretical proprieties of a Nash equilibrium, to develop a program capable of finding all pure Nash equilibria in games with “n” players and “m” strategies (“n” and “m” being finite numbers) as a Macro tool for Microsoft Excel®. It is expected that the program can contributed to the area of Operations Research by providing a new tool that facilitate the use of game theory concepts within group decision-making problem-solving scenarios enabling practical applications using a widespread software.

A decision-making method for consensus building applied to increase the chances of decision implementation in NPOs: the case of fundraising problem

“…Within this spreadsheet, it was also programed the procedures for eliciting the preferences of the directors over the criteria using the Rank Order Centroid (ROC) method, since, according to Barron and Barrett (1996), the ROC method is more appropriate than other rank-based methods for eliciting agents' preferences in group decision making contexts. The Nash equilibrium concept (Nash, 1951) was implemented by the use of the NEFinder add in for Excel (Sugiyama and Leoneti, 2021). Because Nash equilibrium is a mathematical combination that would not have inherent meaning that guarantees commitment of the volunteers a priori, the average of utilities was also adopted for selecting the highest average among the equilibria, representing the so-called method's solution.…”

“…Following, in each standardized decision matrix the Equation 2 was used for calculate the factors of Equation 1 and to calculate the payoff table for each player based on the utility function calculation. Finally, Nash equilibria were searched by means of the NEFinder add-in for Excel (Sugiyama and Leoneti, 2021). For each Nash equilibrium found, the average among the payoffs of Director A, B and C were calculated and ranked in a descending order.…”

Intuitionistic Fuzzy Approch to Triopoly Games

“…A non-linear Intuitionistic fuzzy approach is applied to nd the equilibrium in m × n games [4]. Various methods to nd the Nash Equilibrium in m × n is discussed in [13]. In this paper the Gambit software tool[8] is used to nd the equilibrium solution of the triopoly game.…”