An N-Enterprise Investment Game under Risk of Domino Accidents in a Chemical Cluster: Nash and Pareto Equilibria

Abstract In a chemical cluster, there are a large number of neighboring enterprises, so the risk of accidents faced by an enterprise depends not only on its risk management strategy but also on those of the others in the cluster. To enhance sustainability, each enterprise can choose one of two investment strategies, namely low-level investment and high-level investment for reducing accidents and the resulting losses. Addressing this investment issue using an N-player game, we show that enterprises taking low-level investment might be underpinned by individual and social rationality theoretically. In this game, the enterprises taking low-level investment can be interpreted as free riders as the enterprises taking high-level investment indirectly protect all the enterprises in the cluster from accidents. By free-riding on the high-level investment enterprises against the domino effect of accidents, each low-level investment enterprise can decrease its accident probability. We find that the low-level investment strategy can be both a Nash equilibrium and a Pareto equilibrium. The maximum number of high-level investment enterprises in the cluster depends on the cluster size, as well as the accidental loss and the domino effect of accidents. We also find that enterprises are inclined to take the high-level investment strategy if the accidental loss becomes larger. With an increasing number of enterprises in the cluster, low-level investment is more attractive. The findings in this paper shed light on the sustainability concept of safety investment for enterprises in a chemical cluster.