Make it 'til you fake it

We study the dynamics of fraud and trust in a continuous-time reputation game. The principal wishes to approve a real project and reject a fake. The agent is either an ethical type that produces a real project, or a strategic type that also can produce a fake. Producing a real project takes an uncertain amount of time, while a fake can be created instantaneously at some cost. The unique equilibrium features an initial phase of doubt, during which the strategic agent randomly fakes and the principal randomly approves. Only submissions that arrive after the phase of doubt are beneficial to the principal. We investigate three variants of the model that mitigate this problem. With full commitment, the principal incentivizes the strategic agent to fake at one specific time and commits to approve. Though the principal knows that earlier arrivals are real, she commits to reject them with positive probability. When she can delegate authority, the principal benefits by transferring it to a proxy who is more cautious than she is. When the principal can conduct a costly test prior to her approval decision, the principal also benefits. The equilibrium testing probability may be non-monotonic over time, first increasing, then decreasing.