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.

在化学集群中，有大量的相邻企业，因此，企业面临的事故风险不仅取决于其风险管理策略，而且还取决于集群中其他企业的风险管理策略。为了增强可持续性，每个企业可以选择两种投资策略之一，即低级投资和高级投资，以减少事故和由此产生的损失。使用N解决此投资问题玩家游戏，我们表明，进行低水平投资的企业可能在理论上受到个人和社会理性的支持。在这个游戏中，进行低水平投资的企业可以被解释为搭便车，因为进行高水平投资的企业可以间接保护集群中的所有企业免受意外伤害。通过针对事故的多米诺骨牌效应对高级投资企业实施搭便车，每个低级投资企业都可以降低其发生事故的可能性。我们发现低层次的投资策略既可以是纳什均衡又可以是帕累托均衡。集群中高级投资企业的最大数量取决于集群的规模，以及意外损失和事故的多米诺效应。我们还发现，如果意外损失变大，企业倾向于采取高级投资策略。随着集群中企业数量的增加，低层次的投资更具吸引力。本文的研究结果阐明了化学集群企业安全投资的可持续性概念。