Penalties in the theory of equilibrium tax evasion: Solving King John's problem

We characterize equilibria of an income reporting game with bounded returns and no commitment where detected tax evaders are charged the maximally feasible amount. Introducing partial commitment to punishment relief eliminates multiplicity of equilibria. We identify a unique limit equilibrium where the poorest citizens evade, intermediate citizens are honest and the richest citizens are indifferent between evading and truth-telling. For small tax rates and auditing cost, committing to a discretionary punishment relief scheme increases expected tax revenue.