The intermediary players affect the altruism behavior on the bipartite network

A myriad of participants in the market without direct interactions could act in a coordinated way thanks to the extremely hierarchical and diversified social structures developed spontaneously based on the economic mechanism. This paper investigates the function of the intermediary nodes on the network that may affect the altruistic behavior of the neighbours in the evolutionary games. To achieve this, a pairwise game is proposed on the bipartite graph inspired by the public goods game, where two layers of nodes are defined: the player nodes as the game participants, and the group nodes as the intermediary hubs. Specifically, a tolerance parameter is introduced to modify the behavior of the group nodes, which theoretically raises the surviving threshold of cooperators if sufficiently large. However, a double-edged effect is observed in the experiments where large values of the parameter are applied, which on the one hand helps the cooperators to survive, while it prevents the total elimination of exploiters, indicating the complex relevance between the roles of the intermediary nodes and the system behavior