# Information Design in Non-atomic Routing Games with Partial Participation: Computation and Properties

arXiv: https://arxiv.org/abs/2005.03000 · HTML: https://mlsanity.com/paper/2005.03000/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2020.

## Built on by (most cited first, 3 of 3)

- [Differentiable Bilevel Programming for Stackelberg Congestion Games](https://mlsanity.com/paper/2209.07618/) (2022)
- [Human-in-the-loop Learning for Dynamic Congestion Games](https://mlsanity.com/paper/2404.15599/) (2024)
- [To Analyze and Regulate Human-in-the-loop Learning for Congestion Games](https://mlsanity.com/paper/2501.03055/) (2025)

## Abstract (arXiv)

We consider a routing game among non-atomic agents where link latency functions are conditional on an uncertain state of the network. The agents have the same prior belief about the state, but only a fixed fraction receive private route recommendations or a common message, which are generated by a known randomization, referred to as private or public signaling policy respectively. The remaining agents choose route according to Bayes Nash flow with respect to the prior. We develop a computational approach to solve the optimal information design problem, i.e., to minimize expected social latency over all public or obedient private signaling policies. For a fixed flow induced by non-participating agents, design of an optimal private signaling policy is shown to be a generalized problem of moments for polynomial link latency functions, and to admit an atomic solution with a provable upper bound on the number of atoms. This implies that, for polynomial link latency functions, information design can be equivalently cast as a polynomial optimization problem. This in turn can be arbitrarily lower bounded by a known hierarchy of semidefinite relaxations. The first level of this hierarchy is shown to be exact for the basic two link case with affine latency functions. We also identify a class of private signaling policies over which the optimal social cost is non-increasing with increasing fraction of participating agents for parallel networks. This is in contrast to existing results where the cost of participating agents under a fixed signaling policy may increase with their increasing fraction.