The Uniform Distribution in Incentive Dynamics

The uniform distribution is an important counterexample in game theory as many of the canonical game dynamics have been shown not to converge to the equilibrium in certain cases. In particular none of the canonical game dynamics converge to the uniform distribution in a form of rock-paper-scissors where the amount an agent can lose is more than the agent can win, despite this fact, it is the unique Nash equilibrium. I will show that certain incentive dynamics are asymptotically stable at the uniform distribution when it is an incentive equilibrium. 1 ar X iv :1 20 7. 00 37 v1 [ cs .G T ] 3 0 Ju n 20 12 Incentive dynamics [Fry12] are given by ẋiα = φiα(x)− xiα ∑