Strategic Manipulation Behavior Analysis for Group Decision-Making Based on Nash Bargaining Game and Regret Theory

Group decision-making (GDM) is a crucial approach to ensuring the scientific nature and impartiality of decisions. However, strategic manipulative behaviors driven by self-interested motives often undermine the fairness and effectiveness of decision outcomes, leading to results that deviate from expectations. While most prior studies have focused on theoretical analysis, there remains a significant gap in effective measures to prevent such manipulative behaviors. Moreover, current consensus models predominantly emphasize cost optimization, with less attention paid to the acceptability of feedback. To address these challenges, this study introduces an optimal consensus adjustment mechanism based on the Nash bargaining (NB) solution, aiming to prevent manipulation and self-interested behaviors in GDM. Specifically, we first analyze the opinion manipulation problem within the framework of the minimum adjustment consensus model (MACM). We then construct the Nash product to mitigate the risk of weight manipulation. Subsequently, we examine the nonuniqueness issue in the allocation of minimal total consensus adjustments from the perspective of cooperative game theory. Building on this, we incorporate regret theory to characterize the risk aversion and loss sensitivity of decision-makers (DMs) and propose a consensus adjustment mechanism based on the NB game. Finally, we establish three novel optimization methods to allocate optimal individual consensus adjustments. Case studies and comparative experiments demonstrate the superiority of these methods.