Single-leader-multiple-follower games with boundedly rational agents

This paper studies a class of hierarchical games called single-leader-multiple-follower games (SLMFGs) that have important applications in economics and engineering. We consider such games in the context of boundedly rational agents that are limited in the information and computational power they may possess. Agents in our SLMFG are modeled as adaptive learners that use simple reinforcement learning schemes to learn their optimal behavior. The proposed learning approach is illustrated using a well-studied problem in economics. It is shown that with a patiently learning leader the repeated plays of the game result in approximate equilibrium outcomes.