Designing Network Protocols for Good Equilibria

Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that induce only network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs

Demand-Independent Optimal Tolls

3sìWardrop equilibria in nonatomic congestion games are in general inefficient as they do not induce an optimal flow that minimizes the total travel time. Network tolls are a prominent and popular way to induce an optimum flow in equilibrium. The classical approach to find such tolls is marginal cost pricing which requires the exact knowledge of the demand on the network. In this paper, we investigate under which conditions demand-independent optimum tolls exist that induce the system optimum flow for any travel demand in the network. We give several characterizations for the existence of such tolls both in terms of the cost structure and the network structure of the game. Specifically we show that demand-independent optimum tolls exist if and only if the edge cost functions are shifted monomials as used by the Bureau of Public Roads. Moreover, non-negative demand-independent optimum tolls exist when the network is a directed acyclic multi-graph. Finally, we show that any network with a single origin-destination pair admits demand-independent optimum tolls that, although not necessarily non-negative, satisfy a budget constraint.openopenRiccardo Colini-Baldeschi; Max Klimm; Marco ScarsiniCOLINI BALDESCHI, Riccardo; Klimm, Max; Scarsini, Marc

When Efficiency meets Equity in Congestion Pricing and Revenue Refunding Schemes

Congestion pricing has long been hailed as a means to mitigate traffic congestion; however, its practical adoption has been limited due to the resulting social inequity issue, e.g., low-income users are priced out off certain roads. This issue has spurred interest in the design of equitable mechanisms that aim to refund the collected toll revenues as lump-sum transfers to users. Although revenue refunding has been extensively studied, there has been no thorough characterization of how such schemes can be designed to simultaneously achieve system efficiency and equity objectives. In this work, we bridge this gap through the study of congestion pricing and revenue refunding (CPRR) schemes in non-atomic congestion games. We first develop CPRR schemes, which in comparison to the untolled case, simultaneously (i) increase system efficiency and (ii) decrease wealth inequality, while being (iii) user-favorable: irrespective of their initial wealth or values-of-time (which may differ across users) users would experience a lower travel cost after the implementation of the proposed scheme. We then characterize the set of optimal user-favorable CPRR schemes that simultaneously maximize system efficiency and minimize wealth inequality. These results assume a well-studied behavior model of users minimizing a linear function of their travel times and tolls, without considering refunds. We also study a more complex behavior model wherein users are influenced by and react to the amount of refund that they receive. Although, in general, the two models can result in different outcomes in terms of system efficiency and wealth inequality, we establish that those outcomes coincide when the aforementioned optimal CPRR scheme is implemented. Overall, our work demonstrates that through appropriate refunding policies we can achieve system efficiency while reducing wealth inequality.Comment: This paper was submitted to the inaugural ACM conference on Equity and Access in Algorithms, Mechanisms, and Optimization (EAAMO

Selfish versus coordinated routing in network games

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004.Includes bibliographical references (p. 159-170) and index.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.A common assumption in network optimization models is that a central authority controls the whole system. However, in some applications there are independent users, and assuming that they will follow directions given by an authority is not realistic. Individuals will only accept directives if they are in their own interest or if there are incentives that encourage them to do so. Actually, it would be much easier to let users make their own decisions hoping that the outcome will be close to the authority's goals. Our main contribution is to show that, in static networks subject to congestion, users' selfish decisions drive the system close to optimality with respect to various common objectives. This connection to individual decision making proves fruitful; not only does it provide us with insights and additional understanding of network problems, but it also allows us to design approximation algorithms for computationally difficult problems. More specifically, the conflicting objectives of the users prompt the definition of a network game in which they minimize their own latencies. We show that the so-called price of anarchy is small in a quite general setting. Namely, for networks with side constraints and non-convex, non-differentiable, and even discontinuous latency functions, we show that although an arbitrary equilibrium need not be efficient, the total latency of the best equilibrium is close to that of an optimal solution. In addition, when the measure of the solution quality is the maximum latency, equilibria in networks without constraints are also near-optimal. We provide the first analysis of the problem of minimizing that objective in static networks with congestion.(cont.) As this problem is NP-hard, computing an equilibrium represents a constant-factor approximation algorithm. In some situations, the network authority might still want to do better than in equilibrium. We propose to use a solution that minimizes the total latency, subject to constraints designed to improve the solution's fairness. For several real-world instances, we compute traffic assignments of notably smaller total latency than an equilibrium, yet of similar fairness. Furthermore, we provide theoretical results that explain the conclusions derived from the computational study.by Nicolás E. Stier-Moses.Ph.D

The Impact of Marginal Cost Pricing in Resource Allocation Games

A prelimiary version of this paper titled Efficiency and Stability of Nash Equilibria in Resource Allocation Games appeared in the Proceedings of the First International Conference on Game Theory for Networks (GAMENETS), 2009.We study resource allocation games, where users send data along paths and links in the network charge a price equal to marginal cost. When users are price taking, it is known that there exist distributed dynamics that converge towards a fully efficient Nash equilibrium. When users are price anticipating, however, a Nash equilibrium does not maximize total utility in general. In this paper, we explore the inefficiency of Nash equilibria for general networks and semi-convex marginal cost functions. While it is known that for mgeq 2 users, no efficiency guarantee is possible, we prove that an additional differentiability assumption on marginal cost functions implies a bounded efficiency loss of 2/(2m+1). For polynomial marginal cost functions with nonnegative coefficients we precisely characterize the price of anarchy. We also prove that the efficiency of Nash equilibria significantly improves if all users have the same utility function. We propose a class of distributed dynamics and prove that whenever a game admits a potential function, these dynamics globally converge to a Nash equilibrium. Finally, we show that in general the only} class of marginal cost functions that guarantees the existence of a potential function are affine linear functions

Dynamic traffic congestion pricing mechanism with user-centric considerations

Thesis: S.M. in Transportation, Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 85-95).In this thesis, we consider the problem of designing real-time traffic routing systems in urban areas. Optimal dynamic routing for multiple passengers is known to be computationally hard due to its combinatorial nature. To overcome this difficulty, we propose a novel mechanism called User-Centric Dynamic Pricing (UCDP) based on recent advances in algorithmic mechanism design. The mechanism allows for congestion-free traffic in general road networks with heterogeneous users, while satisfying each user's travel preference. The mechanism first informs whether a passenger should use public transportation or the road network. In the latter case, a passenger reports his maximum accepted travel time with a lower bound announced publicly by the road authority. The mechanism then assigns the passenger a path that matches with his preference given the current traffic condition in the network. The proposed mechanism introduces a fairness constrained shortest path (FCSP) problem with a special structure, thus enabling polynomial time computation of path allocation that maximizes the sequential social surplus and guarantees fairness among passengers. The tolls of paths are then computed according to marginal cost payments. We show that reporting true preference is a weakly dominant strategy. The performance of the proposed mechanism is demonstrated on several simulated routing experiments in comparison to user equilibrium and system optimum.by Kim Thien Bui.S.M. in Transportatio

Robust Methods for Influencing Strategic Behavior

Today's world contains many examples of engineered systems that are tightly coupled with their users and customers. In these settings, the strategic and economic behavior of users and customers can have a significant impact on the performance of the overall system, and it may be desirable for an engineer to devise appropriate methods of incentivizing human behavior to improve system performance. This work seeks to understand the fundamental tradeoffs involved in designing behavior-influencing mechanisms for complex interconnected sociotechnical systems. We study several examples and pose them as problems of game design: a planner chooses appropriate ways to select or modify the utility functions of individual agents in order to promote desired behavior. In social systems these modifications take the form of monetary or other incentives, whereas in multiagent engineered systems the modifications may be algorithmic. Here, we ask questions of sensitivity and robustness: for example, if the quality of information available to the planner changes, how can we quantify the impact of this change on the planner's ability to influence behavior? We propose a simple overarching framework for studying this, and then apply it to three distinct domains: incentives for network routing, distributed control design for multiagent engineered systems, and impersonation attacks in networked systems. We ask the following questions:- What features of a behavior-influencing mechanism directly confer robustness?We show weaknesses of several existing methodologies which use pricing for congestion control in transportation networks. In response to these issues, we propose a universal taxation mechanism which can incentivize optimal routing in transportation networks, requiring no information about network structure or user sensitivities, provided that it can charge sufficiently large prices. This suggests that large prices have more robustness than small ones. We also directly compare flow-varying tolls to fixed tolls, and show that a great deal of robustness can be gained by using a flow-varying approach.- How much information does a planner need to be confident that an incentive mechanism will not inadvertently induce pathological behavior?We show that for simple enough transportation networks (symmetric parallel networks are sufficient), a planner can provably avoid perverse incentives by applying a generalized marginal-cost taxation approach. On the other hand, we show that on general networks, perverse incentives are always a risk unless the incentive mechanism is given some information about network structure.- How can robust games be designed for multiagent coordination?We investigate a setting of multiagent coordination in which autonomous agents may suffer from unplanned communication loss events; the planner's task is to program agents with a policy (analogous to an incentive mechanism) for updating their utility functions in response to such events. We show that even when the nominal game is well-behaved and the communication loss is between weakly-coupled agents, there exists no utility update policy which can prevent arbitrarily-poor states from emerging. We also investigate a setting in which an adversary attempts to influence a distributed system in a robust way; here, by understanding susceptibility to adversarial influence, we hope to inform the design of more robust network systems

Network Game Theory Models of Services and Quality Competition with Applications to Future Internet Architectures and Supply Chains

The Internet has transformed the way in which we conduct business and perform economic and financial transactions. One key challenge of the Internet is the inefficiency of the mechanisms by which technology is deployed and the business and economic models surrounding these processes (Wolf et al. (2014)). Equilibrium models for the Internet generally assume basic economic relationships. However, in new paradigms for the Internet and in supply chain networks, price is not the only factor; quality of service (QoS) is also of increasing importance. Supply chains networks, which give us the means to manufacture products and deliver them to points of demand across the globe, are also under many pressures to offer differentiated products and services (Nagurney (2014)). It is well-known today that success is determined by how well the entire supply chain performs, rather than the performance of its individual entities. This dissertation contributes to the analysis, design, and management of the future Internet and supply chain networks with a focus on price and quality competition in service-oriented networks. Specifically, I focus on economic models for the Internet of the future by developing both a basic and a general network economic game theory model of a quality-based service-oriented Internet to study competition among service providers. To study and analyze the underlying dynamics of the various economic decision-makers, subsequently, I develop a dynamic network economic model of a service-oriented Internet with price and quality competition using projected dynamical systems theory. Then, to assess the prices for various contract durations at the demand markets, I consider a game theory model of a service-oriented Internet in which the network providers compete in usage service rates, quality levels, and duration-based contracts. Finally, I construct a model that captures the competition among manufacturers and freight service providers in a supply chain network. This model is the first one in the literature that handles both price and quality competition with multiple modes of shipment from both equilibrium and dynamic perspectives. For each model, I derive the governing equilibrium conditions and provide the equivalent variational inequality formulations. In order to illustrate the modeling framework and the algorithm, I present computed solutions to several numerical examples for each model as well as sensitivity analysis results. This dissertation is heavily based on the following papers: Saberi, Nagurney, and Wolf (2014), Nagurney et al. (2014a), Nagurney et al. (2015b), and Nagurney et al. (2015a) as well as additional results and conclusions