Sensitivity Analysis for Markov Decision Process Congestion Games

TL;DR

This paper studies how uncertainties and perturbations in congestion costs affect equilibria in Markov decision process congestion games, revealing insights into the stochastic Braess paradox through sensitivity analysis and simulations.

Contribution

It introduces a sensitivity analysis framework for MDP congestion games, analyzing the impact of stochastic dynamics on equilibria and the Braess paradox.

Findings

Sensitivity of equilibria to cost perturbations is characterized.

Stochastic dynamics can amplify or mitigate the Braess paradox.

Simulation results illustrate the effects of uncertainty on congestion outcomes.

Abstract

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.