Contests with multiplicative sabotage effect

This paper investigates a two-player contest with a multiplicative sabotage effect, showing it can be converted into a standard Tullock contest with a nonlinear, endogenous cost function. We prove the existence and uniqueness of a pure strategy equilibrium. Our findings suggest that sabotage activities can be more pronounced when the productivity difference between players is small, and the more productive player might not necessarily undergo more attacks. Lazear and Rosen (1981) first-best outcome is attainable for symmetric players if sabotage is sufficiently ineffective or costly. When it is unattainable, optimal pay difference induces positive sabotage only if sabotage is ineffective but relatively inexpensive. Optimal pay difference decreases with effectiveness and increases with the marginal cost of destructive effort, exhibiting a non-monotonic relationship with productive-effort effectiveness. This non-monotonicity contrasts with the monotonicity of the first best pay difference when sabotage is infeasible.