Enforcing efficient equilibria in network design games via subsidies

TL;DR

This paper explores how subsidies can be used by network designers to enforce efficient network configurations as stable equilibria in selfish user scenarios, addressing the challenge of aligning individual incentives with overall network efficiency.

Contribution

It formulates optimization problems to determine subsidies that enforce or promote efficient equilibria in network design games, providing both positive and negative theoretical results.

Findings

Subsidies can enforce certain network designs as equilibria.

Not all efficient designs can be enforced through subsidies.

The paper identifies conditions where subsidies are effective or ineffective.

Abstract

The efficient design of networks has been an important engineering task that involves challenging combinatorial optimization problems. Typically, a network designer has to select among several alternatives which links to establish so that the resulting network satisfies a given set of connectivity requirements and the cost of establishing the network links is as low as possible. The Minimum Spanning Tree problem, which is well-understood, is a nice example. In this paper, we consider the natural scenario in which the connectivity requirements are posed by selfish users who have agreed to share the cost of the network to be established according to a well-defined rule. The design proposed by the network designer should now be consistent not only with the connectivity requirements but also with the selfishness of the users. Essentially, the users are players in a so-called network design game and the network designer has to propose a design that is an equilibrium for this game. As it is usually the case when selfishness comes into play, such equilibria may be suboptimal. In this paper, we consider the following question: can the network designer enforce particular designs as equilibria or guarantee that efficient designs are consistent with users' selfishness by appropriately subsidizing some of the network links? In an attempt to understand this question, we formulate corresponding optimization problems and present positive and negative results.