Continuous-Time Best-Response and Related Dynamics in Tullock Contests with Convex Costs

TL;DR

This paper proves convergence of continuous-time and related discrete-time best-response dynamics to equilibrium in Tullock contests with convex costs, providing algorithms for equilibrium approximation and validating equilibrium as a predictor of agent behavior.

Contribution

It introduces convergence results for continuous and discrete-time best-response dynamics in Tullock contests with convex costs, along with an equilibrium computation algorithm.

Findings

Convergence of continuous-time best-response dynamics to equilibrium.

Convergence of discrete-time dynamics when responding to empirical averages.

Algorithm for computing approximate equilibrium.

Abstract

Tullock contests model real-life scenarios that range from competition among proof-of-work blockchain miners to rent-seeking and lobbying activities. We show that continuous-time best-response dynamics in Tullock contests with convex costs converges to the unique equilibrium using Lyapunov-style arguments. We then use this result to provide an algorithm for computing an approximate equilibrium. We also establish convergence of related discrete-time dynamics, e.g., when the agents best-respond to the empirical average action of other agents. These results indicate that the equilibrium is a reliable predictor of the agents' behavior in these games.