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 solves 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 MDP. In particular, we show that population mass constraints in MDP congestion games are equivalent to imposing tolls/incentives on the reward function, which can be utilized by social planners to achieve auxiliary objectives. We demonstrate such methods in a simulated Seattle ride-share model, where tolls and incentives are enforced for two separate objectives: to guarantee minimum driver density in downtown Seattle, and to shift the game equilibrium towards a maximum social output.Comment: 7 pages, 6 figures, accepted to American Control Conference 201

Sensitivity Analysis for Markov Decision Process Congestion Games

We consider a non-atomic congestion game where each decision maker performs selfish optimization over states of a common MDP. The decision makers optimize for their own expected costs, and influence each other through congestion effects on the state-action costs. We analyze on the sensitivity of MDP congestion game equilibria to uncertainty and perturbations in the state-action costs by applying an implicit function type analysis. The occurrence of a stochastic Braess paradox is defined, analyzed based on sensitivity of game equilibria and demonstrated in simulation. We further analyze how the introduction of stochastic dynamics affects the magnitude of Braess paradox in comparison to deterministic dynamics