Consensus mechanism with maximum-return modifications and minimum-cost feedback: A perspective of game theory

In group decision making, the interaction behaviors between the moderator and decision makers play a critical role in a consensus process. In this study, based on the essential architecture of Stackelberg game, we present a bi-level optimization model to describe the interaction behaviors between decision makers and moderator, and develop the consensus mechanism with maximum-return modifications and minimum-cost feedback (MRMCCM). In the MRMCCM, the moderator aims to guide decision makers to reach consensus with minimum cost, while decision makers modify their own opinions based on the maximization of individual return. We analyze the equilibrium strategy in the MRMCCM, including the modification and compensation strategies composed of the optimal suggested opinion and unit consensus cost. In addition, an adaptive differential evolution is presented to deal with the bi-level optimization model, and the detailed experimental studies are conducted to justify the performance of the MRMCCM.