Algorithmic Information Design in Multi-Player Games: Possibility and Limits in Singleton Congestion

TL;DR

This paper explores the computational aspects of designing public and private information signals in singleton congestion games, providing efficient algorithms for a fixed number of resources and demonstrating intractability as resources grow.

Contribution

It introduces the first efficient algorithms for exact information design in succinct multi-player congestion games with a fixed number of resources.

Findings

Efficient algorithms for optimal public and private signaling when resources are constant.

Intractability results for large numbers of resources.

Novel techniques for representing equilibria and beliefs in signaling schemes.

Abstract

Most algorithmic studies on multi-agent information design so far have focused on the restricted situation with no inter-agent externalities; a few exceptions investigated truly strategic games such as zero-sum games and second-price auctions but have all focused only on optimal public signaling. This paper initiates the algorithmic information design of both \emph{public} and \emph{private} signaling in a fundamental class of games with negative externalities, i.e., singleton congestion games, with wide application in today's digital economy, machine scheduling, routing, etc. For both public and private signaling, we show that the optimal information design can be efficiently computed when the number of resources is a constant. To our knowledge, this is the first set of efficient \emph{exact} algorithms for information design in succinctly representable many-player games. Our results hinge on novel techniques such as developing certain "reduced forms" to compactly characterize equilibria in public signaling or to represent players' marginal beliefs in private signaling. When there are many resources, we show computational intractability results. To overcome the issue of multiple equilibria, here we introduce a new notion of equilibrium-\emph{oblivious} hardness, which rules out any possibility of computing a good signaling scheme, irrespective of the equilibrium selection rule.