A Novel Game Investment Model on Uniform Hypergraphs

The hypergraph is an excellent tool for describing the investment environment, where hyperedges can be analogies to investment projects and nodes to investors. In addition, it often uses game theory to study investment problems. Therefore, we apply game theory to explore the strategies and benefits of investors in the hypergraph network setting. In this paper, we start from the idea of the group strategy equation in the previous study and propose a discrete node strategy equation on the uniform hypergraph. The equation gives consistent predictions with the results obtained from Monte Carlo simulations, except those at extreme points. Specifically, we explore two different benefit models (equal sharing and dividend sharing models) in this investment model. At the same time, we obtain a relatively counterintuitive conclusion that a higher proportion of decision schemes in investment projects leads to more investors choosing risky strategies when evolving to a steady state. These results can provide help for company decision-making and government regulation-making.