Relative Difference Contest Success Function

Abstract

In this paper we present a Contest Sucess Function (CSF) which is homogeneous of degree zero and where the probabilities of winning the prize depend on the relative difference of efforts. With two agents, we present a necessary and sufficient condition for the existence of a Nash Equilibrium in pure strategies. This equilibrium is unique and interior. This condition does not depend on the size of the valuations as in absolute difference CSF. We prove that several properties of Nash equilibrium and Leader-Follower equilibrium with the Tullock CSF still hold in our framework. Finally, we consider the case of n players, generalize the previous condition and show that it is sufficient for the existence of a unique Nash equilibrium in pure strategies.