Government sanctions to incentivize costly cooperation and deter defection

A government sanctions individuals to cooperate rather than defect when facing adverse situations. Cooperation is costly and may for example entail vaccination against disease or other precautions against risk. The government announces how much it will sanction defectors in stage 1, while individuals cooperate or defect in stage 2. Cooperation increases when sanctions increase relative to the cooperation cost. Individuals have different and probabilistically drawn cooperation costs. The article compares the government’s optimal strategy with the exogenous solutions of mandating cooperation or allowing complete laissez faire. A separating equilibrium is developed where individuals with cooperation costs below some threshold choose to cooperate, while those with higher cooperation costs defect. Equilibrium government sanctions are compared with non-equilibrium government sanctions ranging from no sanctions to maximum sanctions. The fixed-policy two-stage model is extended to an adaptive multi-period model, where sanctions evolve over time based on observed cooperation rates, yielding higher targeted cooperation with modest utility trade-offs. Sanctions to obtain 100% cooperation may be infinitely costly since some individuals may be categorically opposed to cooperation. The article shows how the government may sanction to obtain a specified cooperation percentage when the individuals’ cooperation costs are uniformly distributed. This model provides actionable insights for designing sanction policies to achieve socially optimal cooperation levels, such as high vaccination rates, while minimizing costs to both governments and individuals.