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 learning agents that repeatedly play a "game" on their behalf. We study the dynamics and average outcomes of the repeated game of the agents, and propose to 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 agents by misreporting their parameters to them. We formally define the model of these meta-games between the users for general games and analyze the equilibria induced on the users in two classes of games in which the time-average of all regret-minimizing dynamics converge to a single equilibrium.