Multi-objective programming consensus model based on evolutionary game analysis in group decision making

Consensus-reaching process (CRP) plays an important role in the group decision-making (GDM) process. And CRP is a game between the decision makers (DMs) and the moderator, which involves a series of issues about whether DMs accept the modification suggestions from moderators, how the moderators determine the optimal recommendations and whether compensation is available. To reflect the dynamic interaction between moderators and DMs in CRP, we propose a novel consensus model based on the evolutionary game theory. Specifically, we conduct the strategy stability analysis between DMs and moderators, and prove that there is an evolutionary stable strategy (ESS) with mixed strategies. Then, an ESS-based multi-objective programming consensus model (MOPCM) is developed with the maximum expected utility of DMs and moderators. A non-dominated sorting genetic algorithm is designed to obtain the Pareto solution set containing suggested opinions, adjusted opinions, and the unit adjustment cost. In addition, we provide decision-making guidance for consensus improvement through sensitivity analysis and demonstrate the significance of the evolutionary game between DMs and moderators on CRP.