Evolution of strategies in evolution games on small-world networks and applications

In the game-theoretic model of small-world networks, it is traditionally believed that participants randomly select neighbors to learn from. However, in the era of highly interconnected information, we can regard participants as highly rational individuals who can comprehensively consider the strategies of all their neighbors and adjust their own strategies accordingly to seek the best benefits. From this perspective, we utilize the small-world network model to depict the competitive relationship between participants and propose new strategy updating rules by introducing the Markov transition matrix, aiming to explore the specific impact of the small-world network structure on the cooperation rate of participants. Through simulation analysis, we observe that the behavior of the group tends to evolve towards strategies with higher returns. Among them, the number of neighbors in the network, the initial proportion of cooperative participants, and the potential irrational factor in the updating rules significantly affect the evolution speed of the cooperation rate. It is worth noting that the probability of random reconnection and the number of network nodes have no significant impact on the evolution trend of the cooperation rate. Furthermore, we apply this model to practical scenarios of bidding projects. Combined with a specific analysis of the bidding background, we find that reducing the number of adjacent edges and the initial proportion of cooperative participants are crucial factors in effectively reducing the cooperation rate. This discovery not only provides us with a new perspective to understand cooperative behavior in complex networks, but also offers valuable references for strategy making in actual bidding projects.