Best-Response Dynamics in Lottery Contests

05/18/2023

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by   Abheek Ghosh, et al.

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We study the convergence of best-response dynamics in lottery contests. We show that best-response dynamics rapidly converges to the (unique) equilibrium for homogeneous agents but may not converge for non-homogeneous agents, even for two non-homogeneous agents. For 2 homogeneous agents, we show convergence to an ϵ-approximate equilibrium in Θ(loglog(1/ϵ)) steps. For n ≥ 3 agents, the dynamics is not unique because at each step n-1 ≥ 2 agents can make non-trivial moves. We consider a model where the agent making the move is randomly selected at each time step. We show convergence to an ϵ-approximate equilibrium in O(βlog(n/(ϵδ))) steps with probability 1-δ, where β is a parameter of the agent selection process, e.g., β = n if agents are selected uniformly at random at each time step. Our simulations indicate that this bound is tight.