When countries cope with the risk of disastrous events in a political economy, misperceptions of the damages from the events could occur. We incorporate misperceptions caused by interest groups that have special interests on security spending such as arm-producing companies. If there exists no spillover effect, such misperceptions distort the decision-making of the countries and deteriorate their welfares. However, when countries jointly cope with the risk of disastrous events through the voluntary provision of international public goods, such misperceptions could mitigate inefficiency caused by free-riding behaviors. We show that if the absolute risk aversion of an allied country satisfies certain conditions, the country increases its contribution to the international public good with the overestimation of the damage of a bad event. Furthermore, we show that there could be the optimal value of overestimation, which induces countries to provide the social-welfare-maximizing amounts of international public goods. We also show how the optimal overestimation varies with incomes of the allied countries and their losses in the disastrous events. Finally, we show that if interest groups endogenously determine the magnitude of overestimation, there exists the optimal marginal cost of lobbying inducing the socially optimal overestimation by the interest groups.