# Tolling for Constraint Satisfaction in Markov Decision Process Congestion Games

## TL;DR

This paper introduces tolling mechanisms in Markov decision process congestion games to influence agent behavior, demonstrating their effectiveness in a simulated ride-share environment for achieving specific social objectives.

## Contribution

It establishes a novel connection between population constraints and tolls in MDP congestion games, enabling targeted control of agent strategies.

## Key findings

- Tolls can effectively steer agent behavior in MDP congestion games.
- Tolls help maintain minimum driver density in specific regions.
- Tolls can shift equilibria towards maximizing social output.

## Abstract

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.