Efficient Probabilistic Fines Under Negative Externalities

We introduce a probabilistic fine scheme into a simple model of a public bad with negative externalities. As the fine scheme is probabilistic, an agent’s probability to be fined depends on its relative action level. This induces a counteracting positive externality into the model because the individual fine probability depends not only on own actions but also on the actions of other agents. In our analysis we derive conditions on the primitives of the model that guarantee the existence of an efficient equilibrium where the negative externality of the public bad is neutralised by the positive externality from the fine scheme. We also demonstrate that a fine scheme can always be designed in such a way that an efficient outcome is induced as a pure strategy equilibrium.