  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.
