Framing Effect in Vertex Cover of Networks Under Prospect Theory

Vertex cover (VC) problem is an important combinatorial optimization problem that has a wide range of applications. In this article, we investigate the existing works on solving the VC problem from game theoretic perspective; these works treated each vertex of a network as a completely rational player. In contrast, we consider the impact of player's subjective behavior, that is, each player is not necessarily completely rational. First, we establish a game model under the expected utility theory (EUT) and the framing effect (FE) of the prospect theory. Second, we analyze the relationship between VC and game model under the EUT and the FE. Third, we propose a relaxed greedy behavioral algorithm, and prove that our proposed algorithm can guarantee that the strategies of all vertices converge to a strict Nash equilibrium under the EUT and the FE. Finally, the simulation results not only evaluate the influence of FE on the overall cover level of networks but also demonstrate the effectiveness and superiority of our proposed algorithm compared with the existing bounded rationality algorithm on representative networks and standard benchmark.