Public goods game with the interdependence of different cooperative strategies

Abstract

• A public goods game of two cooperative strategies with different quantities of input cost is proposed. • Two scenarios where different strategies are independent and interdependent are discussed. • If the two strategies are independent, the quasi-defective cost should be reduced to promote the quasi-cooperation. • When the two strategies are interdependent, the indispensability of the quasi-defection sometimes brings to the system more quasi-cooperative agents than when the two strategies are independent. This paper proposes a public goods game (PGG) of two cooperative strategies with different quantities of input cost: the strategy with a higher quantity of input cost is labeled as quasi-cooperation, while that with lower input cost is labeled as quasi-defection. In an ideal classless society, the two strategies are independent, as in the classical PGG; however, in a more realistic class society, they are interdependent. On this basis, two models (An-PGG and In-PGG) are built to respectively describe the two class scenarios. The results for the An-PGG demonstrate that, to promote the quasi-cooperation, the quasi-defective cost should be reduced. The results for the In-PGG indicate that, the closer the two types of input are, the smaller is the difference between the proportions of the two strategies in the system, hence the more effective are the inputs and the greater is the economic benefit. The indispensability of the quasi-defection in an interdependence mechanism sometimes brings to the system more quasi-cooperative agents. The class system is more advantageous than the classless system when the synergy factor and the quasi-defective degree are too small.