Impact of a financial risk-sharing scheme on budget-impact estimations: a game-theoretic approach

As part of the process of updating the National List of Health Services in Israel, health plans (the ‘payers’) and manufacturers each provide estimates on the expected number of patients that will utilize a new drug. Currently, payers face major financial consequences when actual utilization is higher than the allocated budget. We suggest a risk-sharing model between the two stakeholders; if the actual number of patients exceeds the manufacturer’s prediction, the manufacturer will reimburse the payers by a rebate rate of α from the deficit. In case of under-utilization, payers will refund the government at a rate of γ from the surplus budget. Our study objective was to identify the optimal early estimations of both ‘players’ prior to and after implementation of the risk-sharing scheme.

Using a game-theoretic approach, in which both players’ statements are considered simultaneously, we examined the impact of risk-sharing within a given range of rebate proportions, on players’ early budget estimations.

When increasing manufacturer’s rebate α to be over 50 %, then manufacturers will announce a larger number, and health plans will announce a lower number of patients than they would without risk sharing, thus substantially decreasing the gap between their estimates. Increasing γ changes players’ estimates only slightly.

In reaction to applying a substantial risk-sharing rebate α on the manufacturer, both players are expected to adjust their budget estimates toward an optimal equilibrium. Increasing α is a better vehicle for reaching the desired equilibrium rather than increasing γ, as the manufacturer’s rebate α substantially influences both players, whereas γ has little effect on the players behavior.