Hide or show? Endogenous observability of private precautions against crime when property value is private information

This paper analyzes a contest in which defenders move first, have private information about the value of the objects they are trying to protect, and determine the observability of their defense efforts. The equilibrium consistent with the intuitive criterion depends on the distribution of defender types, the magnitude of the difference between defender types, and the asymmetry between defender and aggressor regarding the valuation of the objects at stake in the contest. Our setting captures key characteristics of the interaction between households and thieves, focusing on the classic distinction between observable and unobservable private precautions against crime. An analysis of welfare implications determines that a setting in which information about the value of the protected objects is private results in a better outcome than a complete-information scenario.