A framework for accessing the equilibrium point of a multi-objective decision-making (MODM): a case study

In recent years, equilibrium is the most generally used solution concept in game theory. This idea may be a state-of-the-art interpretation of a method game. Each player has an accurate prediction of other players’ behavior and acts consistent with such a rational prediction. This paper aims to apply the game theory idea of equilibrium as a decision-making tool to develop a simple method for solving a multi-objective decision-making problem with any number of players to achieve an equilibrium point. Game theory and Nash equilibrium have been used to determine the equilibrium point of multi-objective decision-making problems of production planning in non-cooperative environments. A mixed and conditional N-player model was proposed as a development of the Nash model. The method was applied to a second-square planning problem with multiple constrained objectives (with linear constraints) in order to allocate a larger share of the sales market in a situation where all objectives were in conflict with each other. Effective solutions were first obtained using the b l constraint method, and then, an effective equilibrium point was extracted using the proposed method. Since the problem-solving method was discrete, the effective equilibrium point was reduced, and the results were used for making decisions about six products in the competitive market.