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Under the Markov decision process (MDP) congestion game framework, we studythe problem of enforcing population distribution constraints on a population ofplayers with stochastic dynamics and coupled congestion costs. Existingresearch demonstrates that the constraints on the players' populationdistribution can be satisfied by enforcing tolls. However, computing theminimum toll value for constraint satisfaction requires accurate modeling ofthe player's congestion costs. Motivated by settings where an accuratecongestion cost model is unavailable (e.g. transportation networks), weconsider an MDP congestion game with unknown congestion costs. We assume that aconstraint-enforcing authority can repeatedly enforce tolls on a population ofplayers who converges to an $\epsilon$-optimal population distribution for anygiven toll. We then construct a myopic update algorithm to compute the minimumtoll value while ensuring that the constraints are satisfied on average. Weanalyze how the players' sub-optimal responses to tolls impact the rates ofconvergence towards the minimum toll value and constraint satisfaction.Finally, we construct a congestion game model for Uber drivers in Manhattan,New York City (NYC) using data from the Taxi and Limousine Commission (TLC) toillustrate how to efficiently reduce congestion while minimizing the impact ondriver earnings.

Adaptive Constraint Satisfaction for Markov Decision Process Congestion Games: Application to Transportation Networks