Asymmetric contests with risky rents

We study a rent-seeking proprtional-prize contest between two heterogeneously risk-averse players and given prize amounts are normally distributed rather than known ex ante. We establish existence and unicity of a Nash equilibrium linked to this contest, and study the equilibrium e_orts implied. We then obtain a similar equilibrium result for a winner-takes-all lottery contest within the same risky rent context, and compare optimal e_orts as well as expected utilities between the two contest types.