A Minimal Memory Game-based Distributed Algorithm to Vertex Cover of Networks

The vertex cover of networks is a classical combinatorial optimization problem. In this paper, we investigate the vertex cover problem solved by the memory-based best response update rule, which can not converge to a strict Nash equilibrium (SNE) with memory length m = 1. To overcome this shortcoming, a bounded rational behavioral (BRB) update rule is newly proposed in this paper. We prove that the BRB with m = 1 can guarantee that the whole vertices' state converges to a SNE. The simulation is carried out to verify that the performance of the proposed BRB update rule on representative networks. Moreover, we also find that a better SNE will be achieved by increasing the selection intensity.