Contests with productive effort

I consider competitions in which, conditional on winning or losing, the effort exerted by a competitor does not necessarily decrease his payoff. This happens, for example, in competitions for promotions in which workers are intrinsically motivated, and in research and development races in which better performance implies a higher payoff from winning. I characterize players' equilibrium payoffs in closed form, thereby generalizing Siegel (Econometrica 77(1):71-92, 2009) payoff result to contests in which players' payoff functions are non-monotonic.