| Abstract: |
We study a repeated sender–receiver game where inspections are public but the
sender’s action is hidden unless inspected. A detected deception ends the
relationship or triggers a finite punishment. We show the public state is
low-dimensional and prove existence of a stationary equilibrium with cutoff
inspection and monotone deception. The sender’s mixing pins down a closed-form
total inspection probability at the cutoff, and a finite punishment phase
implements the same cutoffs as termination. We extend to noisy checks, silent
audits, and rare public alarms, preserving the Markov structure and continuity
as transparency vanishes or becomes full. The model yields testable
implications for auditing, certification, and platform governance: tapering
inspections with reputation, bunching of terminations after inspection spurts,
and sharper cutoffs as temptation rises relative to costs. |