Towards a Snowdrift Game Optimization to Vertex Cover of Networks

Abstract

To solve the vertex cover problem in an agent-based and distributed networking systems utilizing local information, we treat each vertex as an intelligent rational agent rather than an inanimate one and provide a spatial-snowdrift-game-based optimization framework to vertex cover of networks. We analyze the inherent relation between the snowdrift game and the vertex cover: Strict Nash equilibriums of the spatial snowdrift game are the intermediate states between vertex-covered and minimal-vertex-covered states. Such equilibriums are obtained by employing the memory-based best response update rule. We also find that a better approximate solution in terms of the minimal vertex cover will be achieved by increasing the individuals' memory length, because such a process optimizes the individuals' strategies and helps them convert from bad equilibriums into better ones. Our findings pave a new way to solve the vertex cover problem from the perspective of agent-based self-organized optimization.

Probability weighting effect in vertex cover of networks via prospect-theoretic learning

“…To seek the minimum vertex cover of a network, various distributed optimization algorithms have been proposed, mainly from the perspective of the game-based distributed algorithms, where each vertex is regarded as a player. For example, Yang et al first used a snowdrift game to describe the vertex cover problem, and presented a memory-based best response distributed algorithm, which can guarantee to obtain a strict Nash equilibrium (SNE) [5]. After then, Tang et al studied a variant of the vertex cover problem, that is, the weighted vertex cover (WVC) problem, and modeled the problem as an asymmetric game model, and proposed a feedback-based best response algorithm, and obtained a SNE [6].…”

“…To sum up, the works in [5]- [8] studied the (weighted) vertex cover problem from game theoretic perspective. A common assumption is that all players in the game are completely rational and make appropriate strategies as long as their objective expected functions can be optimized, this assumption is based on expected utility theory.…”