Tolling for Constraint Satisfaction in Markov Decision Process Congestion Games

Markov Decision Process (MDP) congestion game is an extension of classic congestion games, where a continuous population of selfish agents each solves a Markov decision processes with congestion: the payoff of a strategy decreases as more population uses it. We draw parallels between key concepts from capacitated congestion games and MDPs. In particular, we show that the population mass constraints in MDP congestion games are equivalent to imposing tolls/incentives on the reward function, which can be utilized by a social planner to achieve auxiliary objectives. We demonstrate such methods on a simulated Seattle ride-share model, where tolls and incentives are enforced for two distinct objectives: to guarantee minimum driver density in downtown Seattle, and to shift the game equilibrium towards a maximum social output.