Robustness of Learning in Games With Heterogeneous Players

We consider stochastic learning dynamics in games and present a novel notion of robustness to heterogeneous players for a stochastically stable action profile. A standard assumption in these dynamics is that all the players are homogeneous, and their decision strategies can be modeled as perturbed versions of myopic best or better response strategies. We relax this assumption and propose a robustness criteria, which characterizes a stochastically stable action profile as robust to heterogeneous behaviors if a small fraction of heterogeneous players cannot alter the long-run behavior of the rest of the population. In particular, we consider confused players who randomly update their actions, stubborn players who never update their actions, and strategic players who attempt to manipulate the population behavior. We establish that radius-coradius based analysis can provide valuable insights into the robustness properties of stochastic learning dynamics for various game settings. We derive sufficient conditions for a stochastically stable profile to be robust to a confused, stubborn, or strategic player and elaborate these conditions through carefully designed examples. Then we explore the role of network structure in our proposed notion of robustness by considering graphical coordination games and identifying network topologies in which a single heterogeneous player is sufficient to alter the population's behavior. Our results will provide foundations for future research on designing networked systems that are robust to players with heterogeneous decision strategies.