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.