Robustness of Incentive Mechanisms Against System Misspecification in Congestion Games

TL;DR

This paper investigates how small inaccuracies in system models affect toll strategies in congestion games, showing that minor misspecifications do not create new equilibria and bounding performance degradation.

Contribution

It provides theoretical guarantees on the robustness of toll designs against minor system misspecifications in atomic congestion games.

Findings

Minor misspecifications do not create new Nash equilibria.

Bounds on worst-case performance degradation are established.

Theoretical results are validated through simulations.

Abstract

To steer the behavior of selfish, resource-sharing agents in a socio-technical system towards the direction of higher efficiency, the system designer requires accurate models of both agent behaviors and the underlying system infrastructure. For instance, traffic controllers often use road latency models to design tolls whose deployment can effectively mitigate traffic congestion. However, misspecifications of system parameters may restrict a system designer's ability to influence collective agent behavior toward efficient outcomes. In this work, we study the impact of system misspecifications on toll design for atomic congestion games. We prove that tolls designed under sufficiently minor system misspecifications, when deployed, do not introduce new Nash equilibria in atomic congestion games compared to tolls designed in the noise-free setting, implying a form of local robustness. We then upper bound the degree to which the worst-case equilibrium system performance could decrease when tolls designed under a given level of system misspecification are deployed. We validate our theoretical results via Monte-Carlo simulations as well as realizations of our worst-case guarantees.