The Uniform Distribution in Incentive Dynamics

TL;DR

This paper investigates the stability of the uniform distribution in game theory, showing that certain incentive dynamics can be asymptotically stable at this equilibrium despite canonical dynamics failing to converge.

Contribution

It demonstrates that specific incentive dynamics are asymptotically stable at the uniform distribution, expanding understanding of equilibrium stability in game dynamics.

Findings

Certain incentive dynamics are asymptotically stable at the uniform distribution.

Canonical game dynamics do not converge to the uniform distribution in rock-paper-scissors.

The uniform distribution can be an incentive equilibrium with stability properties.

Abstract

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.