A Biobjective Biform Game Approach to Optimizing Strategies in Bilateral Link Network Formation.

The purpose of this article is to present a novel biobjective biform game framework for optimizing strategy selection of nodes (agents) in bilateral link network formation under dual objectives of profit and link security. First, in the first part of the noncooperative game, we construct various possible strategy combinations (situations) of all players (nodes) in the network, which define the competitive environment in the second part of the cooperative game. Second, in the second part, we derive coalitions’ payoffs under the two objectives of profit and link security and propose the biobjective Banzhaf values to allocate the corresponding cooperative games in all strategy situations. Then, a biobjective noncooperative game is formed on the basis of the obtained biobjective Banzhaf values. Third, we redefine Pareto–Nash equilibriums (in the sense of pure strategies) and obtain the Pareto–Nash equilibriums of the biobjective noncooperative game in the first part. Subsequently, the choice of the obtained Pareto–Nash equilibriums is regarded as a biobjective group decision-making problem, which is solved by employing the redefined Borda choice function method with objective weights. Hence, we can obtain the optimal strategy choices of all the nodes (players) for the entire bilateral link network formation. Finally, numerical examples and comparative analysis are given to verify the validity and applicability of the proposed models and methods. [ABSTRACT FROM AUTHOR]