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The most significant problems in financing the public health system in Ukraine are the permanent deficit of public spending on medicine and the shallow development of the voluntary health insurance market. The aim of study is the search of optimal interactions between stakeholders in the system of relations “state–insurance companies–households” in the context of voluntary health insurance. The study hypothesizes that households can become more active participants in health insurance only if their average monthly income reaches a certain threshold level. It is calculated based on the results of simulation games using the Brown-Robinson iterative method. According to the simulation results, this threshold level is only 7% higher than the actual value of the average monthly income of Ukrainian households during the analysis. At the same time, under this condition, the state in Ukraine will be able to transfer part of the financial burden of compensating healthcare costs to insurance companies. According to the calculations made with the help of the game theory toolkit, with the maximization of insurance payments to the population under health insurance contracts, the burden on public health financing in Ukraine could be reduced by 67.7%. The paper was conducted on the data of the ten most potent insurance companies of Ukraine as of 2021 (it is they who accumulate the lion’s share of household insurance premiums), that is, before the start of a full-scale war between the Russian Federation and Ukraine. The obtained results can be used both by insurance companies during the management of insurance premiums and payments and at the …