Signaling in Bayesian Network Congestion Games: the Subtle Power of Symmetry

TL;DR

This paper investigates how signaling can influence congestion game outcomes, showing that symmetry allows for polynomial-time optimal signaling schemes, while asymmetry leads to computational hardness.

Contribution

It demonstrates that symmetric players enable efficient computation of optimal signaling, whereas asymmetry makes the problem NP-hard, highlighting the importance of symmetry in network information design.

Findings

Optimal ex ante persuasive signaling schemes are computable in polynomial time for symmetric players.

The problem is NP-hard for asymmetric players, even without Bayesian uncertainty.

Symmetry plays a crucial role in the tractability of signaling in congestion games.

Abstract

Network congestion games are a well-understood model of multi-agent strategic interactions. Despite their ubiquitous applications, it is not clear whether it is possible to design information structures to ameliorate the overall experience of the network users. We focus on Bayesian games with atomic players, where network vagaries are modeled via a (random) state of nature which determines the costs incurred by the players. A third-party entity---the sender---can observe the realized state of the network and exploit this additional information to send a signal to each player. A natural question is the following: is it possible for an informed sender to reduce the overall social cost via the strategic provision of information to players who update their beliefs rationally? The paper focuses on the problem of computing optimal ex ante persuasive signaling schemes, showing that symmetry is a crucial property for its solution. Indeed, we show that an optimal ex ante persuasive signaling scheme can be computed in polynomial time when players are symmetric and have affine cost functions. Moreover, the problem becomes NP-hard when players are asymmetric, even in non-Bayesian settings.