Network game in group decision making: Managing consensus with incentive and interaction interventions

For a group of interactive decision makers (DMs), reaching consensus requires not only mutual communication among them but also the input from an external entity (moderator), such as preference adjustment suggestions and incentive interventions. Traditional consensus mechanisms that compel DMs to passively accept adjustment suggestions may pose several obstacles, such as democratic concerns, insufficient practicability and low-acceptance issues. To better ensure the achievement of the consensus-reaching process (CRP), this paper attempts to stimulate DMs' subjective initiative in preference adjustments by exploiting peer effects and external incentives. Under targeted incentives from the external entity, DMs interact with each other to adjust their preferences strategically for utility maximization. We formulate DMs' adjustment behaviors as a network game with peer effects and then propose a network game-based consensus mechanism. From this game, DMs' preference adjustments in equilibrium are derived and their structural properties are correspondingly examined. Then, a comparative analysis is conducted between equilibria with and without peer effects to specify the network synergy. Next, we design two equilibrium adjustment-enabled consensus models through interventions on interaction links and incentive rates. Finally, several numerical examples and simulations are presented to illustrate and extend our theoretical results. In addition to mathematical models and analysis, this paper also provides insights into consensus management.