Global inspection games

• We model an inspection game with common shocks and costly message verification.
• Unlike the cut-off rule (COR), the Optimal Inspection Strategy (OIS) creates a coordination game.
• Agents are imperfectly informed about the inspector’s type.
• Thus, game can be realistically modeled as a global game. Equilibrium is unique.
• OIS yields less targeting errors than the traditionally prescribed COR. Predictions are supported by experimental data.

In the tax evasion game – a typical example of “inspection game” – audits are costly and audit probabilities are determined by the tax agency based on the tax returns submitted by taxpayers. We find that if taxpayers' incomes are correlated (e.g., when they are subject to a common shock) the optimal audit probability for low declarations is an increasing function of the average declaration, as the latter is an informative signal of the realized level of income. Since a taxpayer's optimal declaration is an increasing function of the probability of an audit, the optimal auditing rule creates incentives for taxpayers to coordinate their declarations. The resulting coordination game features multiplicity of equilibria and thus “strategic uncertainty” about the equilibrium that will be selected.When we add a source of “fundamental uncertainty” (about the type of agency taxpayers face), the situation can be realistically modeled as a global game. Further, and unlike the coordination game before, it yields a unique – and usually interior – equilibrium which is consistent with empirical evidence and supported by the data collected in a computerized experiment.The model can be applied to other “inspection games” of economic interest such as the regulation of industries and the allocation of welfare benefits, among others.