Evolutionary game dynamics of index insurance with refund or non-refund risk sharing mechanism

Index insurance, by utilizing preset indices, effectively mitigates the moral hazards and adverse selection inherent in traditional insurance. Yet, the mismatch between these indices and actual losses, known as basis risk, severely hinders its broader adoption. The existing study has proposed a risk sharing mechanism, in which individuals who have not suffered losses but have received compensation assist those who have suffered losses but have not received compensation. Nonetheless, due to individual profit-seeking behavior, this mechanism is difficult to implement in practice. In this study, we construct a threshold-discounted index insurance game model including new risk sharing mechanisms. In the model, individuals purchasing index insurance are required to contribute to a risk sharing pool to compensate those facing basis risk. We analyze two mechanisms for handling the funds: a refund mechanism and a non-refund mechanism, depending on whether the funds are returned to the policyholders when no basis risk occurs. We find that low basis risk remains key for the sale of index insurance under both mechanisms. Moreover, with an appropriate risk sharing ratio, the introduction of a risk sharing pool significantly increases the adoption of index insurance. The refund mechanism, with its stronger risk sharing capability, proves more popular. Additionally, larger group sizes or lower collective thresholds can enhance the stability and aid capacity of the risk sharing pool, thereby further increasing adoption rates. Finally, insurance companies should accurately assess the risk aversion level of the population, as it is also a key factor affecting insurance sales.