A novel bilateral protocol in the bipartite network based on the public goods game

Abstract

Games with more than two participants are less efficient to establish or maintain than traditional pairwise games, because each player is obliged to gather the information of multiple partners before formulating strategies or figuring out the results. In reality, exchanges between only two individuals are predominant in economic activities, for example, the transaction between a retailer and a consumer, a loaner and a loanee, an employer and an employee, etc. Generally, a highly hierarchical and diversified structure is developed in the economic system which coordinates the mutual supply between entities without direct contacts. This work investigates the public goods game on the bipartite network, where the multilateral correlations in the groups are substituted by bilateral ones between the heterogeneous nodes from a two-layer hierarchy: the layer of normal players, and the layer of group nodes denoting the groups. Strategies are selected by each type of nodes with different frequency and method. Specifically, three strategy updating protocols are designed for the group nodes. In the most fundamental condition, the game is identical to the classic public goods game. However, when alternative protocols are applied, the cooperation tendency is influenced significantly, which is a phenomenon cannot be observed in traditional public goods games on homogeneous networks. The pair approximation method is employed to predict the cooperation tendency of the system. Furthermore, the theoretic conclusion is verified in the simulation, meanwhile the factors that affect the altruism behavior are investigated.