Reasons to grant immigration amnesties include the intention to reduce the weight of the informal sector and the attempt to identify employers of undocumented workers. However, it is incontestable that potential fiscal gains are important: tax revenues are crucial in all kinds of amnesties. Nevertheless, over the last 30 years 24% of applications have been rejected. It is still unexplained why governments accept this loss of fiscal base. We argue that applying for amnesty is basically selfincrimination, and that immigration-averse governments have an incentive to exploit the applications to identify and expel illegal workers. In our Nash equilibrium only applicants with the highest income are granted amnesty, and the poorest immigrants do not apply. In addition, it is not possible to establish a reputation because the players are different every time the game is repeated. Thus, fiscal revenues are sub-optimal and amnesties are an inefficient way to make illegal workers come forward.