Incorporation an algorithm for search of the Nash equilibrium in method of multicriteria decision-making

Abstract

To assist managers in their decision making, the use of methods to support decision making has been used since the 1950s, with strong emphasis on assessment of economic and financial issues and operational. The praxis of most of these methods is based on the decision maker as an individual, and the use of these methods in multicriteria decision making in groups has been proposed with adding vectors. However, despite being a common practice, aggregation can conceal conflicts. Within this context, Leoneti (2012) proposed a multi-criteria method, with the application of game theory and the Nash Equilibrium, considering the conflict of interests in decision-making in a group environment and incorporates the strategies adopted by decision makers to establishing a compromise, without the use of traditional way of adding weights. However, having only been applied to a case study of choice for sewage treatment system, the method should still be examined dynamically through simulations and experiments implemented, to prove the existence of a critical and innovative feature: the convergence of solutions for balance. Due to the fact that the method was implemented in an Excel spreadsheet and need an external software to perform the search for the Nash equilibrium, this project proposes to incorporate an algorithm for seeking the Nash equilibrium within the spreadsheet, which allow verification stability of the method by means of simulations. Moreover, tests based on actual situations of choice in the group are applied to check the balance involving all aspects of the game actually increases the chances of finding a sustainable solution that satisfies the preferences of most involved.