How and Why to Manipulate Your Own Agent

We consider strategic settings where several users engage in a repeated online interaction, assisted by regret-minimizing agents that repeatedly play a "game" on their behalf. We study the dynamics and average outcomes of the repeated game of the agents, and view it as inducing a meta-game between the users. Our main focus is on whether users can benefit in this meta-game from "manipulating" their own agent by mis-reporting their parameters to it. We formally define this "user-agent meta-game" model for general games, discuss its properties under different notions of convergence of the dynamics of the automated agents and analyze the equilibria induced on the users in 2x2 games in which the dynamics converge to a single equilibrium.