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.

翻译：图洛克竞赛模拟了从工作量证明区块链矿工竞争到寻租与游说活动等现实场景。我们通过李雅普诺夫型论证表明，在具有凸成本的图洛克竞赛中，连续时间最佳响应动力学收敛至唯一均衡。进而利用这一结果为计算近似均衡提供了算法。我们还建立了相关离散时间动力学的收敛性，例如当智能体对其他智能体的经验平均行动做出最佳响应时。这些结果表明，均衡是这些博弈中智能体行为的可靠预测指标。