Endogenous enforcement cycles. The co-evolution of tax evasion and audit strategies

This paper studies tax enforcement as a governance problem in which taxpayer compliance and administrative monitoring are jointly endogenous. We formalize this interaction in a two-population evolutionary game between taxpayers, who choose whether to comply or under-declare income, and authority-side enforcement units, which choose whether to inspect. Inspection is costly and imperfectly effective, and the authority side may internalize recoverable but unrecovered tax losses as an institutional-performance loss. The model identifies an interior enforcement benchmark linking tax rates, penalties, audit effectiveness, inspection costs, and institutional accountability. Under canonical replicator dynamics, this benchmark is not a stable endpoint but the center of recurrent compliance–enforcement cycles: evasion raises audit incentives, audits increase compliance, compliance weakens monitoring incentives, and weaker monitoring reopens space for evasion. Numerical illustrations show how enforcement design affects compliance, inspection, recoverable tax losses, net revenue, and institutional performance. The paper highlights that tax governance outcomes depend not only on sanctions but also on the incentives that sustain monitoring effort over time.