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Robustness of Incentive Mechanisms Against System Misspecification in Congestion Games

Chih-Yuan Chiu, Bryce L. Ferguson

TL;DR

The paper addresses how misspecified system parameters affect toll design in atomic congestion games. It proves that sufficiently small parameter errors do not generate new Nash equilibria under designed tolls, establishing local robustness, and develops a linear program to bound the worst-case PoA under relative parameter perturbations. The authors validate these results on a Sioux Falls–style network and affine-cost games, revealing that PoA can grow with misspecification but remains bounded within the proposed framework. They also compare toll strategies and highlight non-monotone robustness with respect to toll magnitude, motivating robust toll design as a practical priority.

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.

Robustness of Incentive Mechanisms Against System Misspecification in Congestion Games

TL;DR

The paper addresses how misspecified system parameters affect toll design in atomic congestion games. It proves that sufficiently small parameter errors do not generate new Nash equilibria under designed tolls, establishing local robustness, and develops a linear program to bound the worst-case PoA under relative parameter perturbations. The authors validate these results on a Sioux Falls–style network and affine-cost games, revealing that PoA can grow with misspecification but remains bounded within the proposed framework. They also compare toll strategies and highlight non-monotone robustness with respect to toll magnitude, motivating robust toll design as a practical priority.

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.
Paper Structure (8 sections, 5 theorems, 19 equations, 3 figures, 1 table)

This paper contains 8 sections, 5 theorems, 19 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Sensitivity of Nash Equilibrium Strategy Set to Cost Parameters
  4. LP for Robust PoA Computation
  5. Experimental Results
  6. Sensitivity of Nash Equilibrium Strategy Set
  7. Simulations of LPs for Toll Robustness
  8. Conclusion and Future Work

Key Result

Proposition 1

Given any $\gamma \in \mathbb{R}_{\geq 0}^{|E|m}$, there exists some $\epsilon > 0$ such that, for any $\tilde{\gamma} \in \mathbb{R}_{\geq 0}^{|E|m}$ satisfying $|\tilde{\gamma}_{e,j} - \gamma_{e,j}| \leq \epsilon$ for each $e \in E, j \in [m]$:

Figures (3)

  • Figure 1: A simplified Sioux Falls network model in which commuters travel from an origin node (blue, indexed 1) to a destination node (red, indexed 7). The model contains 5 routes sharing 10 edges and 7 nodes.
  • Figure 2: Evaluation, using Prop. \ref{['Prop:LP_relative_error']}, of the PoA realized in congestion games with affine resource costs when tolls designed with relative latency parameter error $\delta$ are deployed. We consider the marginal cost toll meir2016marginal, the optimal local toll Paccagnan2021OptimalTaxesinAtomicCongestionGames Thm. 1, and the optimal local fixed toll Paccagnan2021OptimalTaxesinAtomicCongestionGames mechanisms.
  • Figure 3: The PoA bound in congestion games with affine resource costs, as computed via Prop. \ref{['Prop:LP_relative_error']}, of $T_\lambda(\ell) = \lambda(\ell+T(\ell))-\ell$ where $T$ is the optimal local toll mechanism computed in Paccagnan2021OptimalTaxesinAtomicCongestionGames.

Theorems & Definitions (9)

  • Definition 1
  • Proposition 1
  • proof
  • Corollary 1
  • proof
  • Corollary 2
  • Corollary 3
  • Proposition 2
  • proof