Enforcing Efficient Equilibria in Network Design Games via Subsidies

Abstract

International audienceThe 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

Cost Minimization for Equilibrium Transition

“…Monderer and Tennenholtz (2009) propose to use mediators in order to enrich the set of situations where one can obtain stability against deviations by coalitions, in light of the understanding that strong equilibrium rarely exists. Augustine et al (2015) address the question of whether a network designer can enforce particular equilibria or guarantee that efficient designs are consistent with users' selfishness by appropriately subsidizing some of the network links. They formulate this question as one of the optimization problems and present positive and negative results.…”

Truthfulness on a budget: trading money for approximation through monitoring

“…However, in some applications, it is reasonable to adopt mechanisms that do not satisfy this property and therefore it makes sense to consider the necessity of B * for those mechanisms. For instance, drawing a parallel with the setting where subsidies are employed to enforce efficient equilibria, [1,4,5], relaxing individual rationality is equivalent to provide partial subsidies that do not cover the whole cost of the equilibrium solution. We pursue this research direction in the remainder of the paper.…”

“…In [4] a cost sharing system is studied where users purchase public services equally sharing their cost, and a central authority enforces "good" purchasing choices by reinvesting tax revenue in the form of subsidies to the public services. In [1] Augustine at al. study network design games where a set of agents share the cost of building edges on a network, and subsidies (partially) cover the cost of some of the edges included in the equilibrium spanning tree.…”

“…In detail, we look at mechanisms with monitoring, studied in [13,17,18]. 1 Mechanisms with monitoring assume that the designer is able to monitor the agents' costs so to guarantee that the agents who have exaggerated theirs end up paying the reported (higher) cost. Intuitively, it is assumed that the designer can 'watch' the agents at "work" and force them to spend more than their real cost, if they overbid.…”

Efficiency and complexity of price competition among single-product vendors

“…The (apparently non-exhaustive) list also includes their use in cooperative game theory in order to encourage coalitions of players to reach stability [5] and as a means to stabilize normal form games [19]. As in [2] and [7], the use of monetary incentives in the current paper aims to improve efficiency. Monetary disincentives like taxes have been used to improve the efficiency of network routing (see [9] and the references therein for a relatively recent approach that extends early developments in the literature of the economics of transportation) and, in the recent AI literature, in boolean games [23].…”