We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

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Convex Analysisの二,三の進展について

This exciting and pioneering new overview of multiagent systems, which are online systems composed of multiple interacting intelligent agents, i.e., online trading, offers a newly seen computer science perspective on multiagent systems, while integrating ideas from operations research, game theory, economics, logic, and even philosophy and linguistics. The authors emphasize foundations to create a broad and rigorous treatment of their subject, with thorough presentations of distributed problem solving, game theory, multiagent communication and learning, social choice, mechanism design, auctions, cooperative game theory, and modal logics of knowledge and belief. For each topic, basic concepts are introduced, examples are given, proofs of key results are offered, and algorithmic considerations are examined. An appendix covers background material in probability theory, classical logic, Markov decision processes and mathematical programming. Written by two of the leading researchers of this engaging field, this book will surely serve as THE reference for researchers in the fastest-growing area of computer science, and be used as a text for advanced undergraduate or graduate courses.

Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations

Selfish routing is a classical mathematical model of how self-interested users might route traffic through a congested network. The outcome of selfish routing is generally inefficient, in that it fails to optimize natural objective functions. The price of anarchy is a quantitative measure of this inefficiency. We survey recent work that analyzes the price of anarchy of selfish routing. We also describe related results on bounding the worst-possible severity of a phenomenon called Braess's Paradox, and on three techniques for reducing the price of anarchy of selfish routing. This survey concentrates on the contributions of the author's PhD thesis, but also discusses several more recent results in the area.

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Selfish Routing and the Price of Anarchy

This is the first comprehensive critical evaluation of the use of rational choice theory in political science. Writing in an accessible and nontechnical style, Donald P. Green and Ian Shapiro assess rational choice theory where it is reputed to be most successful: the study of collective action, the behavior of political parties and politicians, and such phenomena as voting cycles and Prisoner's Dilemmas. In their hard-hitting critique, Green and Shapiro demonstrate that the much heralded achievements of rational choice theory are in fact deeply suspect and that fundamental rethinking is needed if rational choice theorists are to contribute to the understanding of politics. In their final chapters, they anticipate and respond to a variety of possible rational choice responses to their arguments, thereby initiating a dialogue that is bound to continue for some time.

Pathologies of rational choice theory: A critique of applications in political science.

According to Wardrop's first principle, agents in a congested network choose their routes selfishly, a behavior that is captured by the Nash equilibrium of the underlying noncooperative game. A Nash equilibrium does not optimize any global criterion per se, and so there is no apparent reason why it should be close to a solution of minimal total travel time, i.e., the system optimum. In this paper, we offer positive results on the efficiency of Nash equilibria in traffic networks. In contrast to prior work, we present results for networks with capacities and for latency functions that are nonconvex, nondifferentiable, and even discontinuous.The inclusion of upper bounds on arc flows has early been recognized as an important means to provide a more accurate description of traffic flows. In this more general model, multiple Nash equilibria may exist and an arbitrary equilibrium does not need to be nearly efficient. Nonetheless, our main result shows that the best equilibrium is as efficient as in the model without capacities. Moreover, this holds true for broader classes of travel cost functions than considered hitherto.

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Selfish Routing in Capacitated Networks

The design of route guidance systems faces a well-known dilemma. The approach that theoretically yields the system-optimal traffic pattern may discriminate against some users in favor of others. Proposed alternate models, however, do not directly address the system perspective and may result in inferior performance. We propose a novel model and corresponding algorithms to resolve this dilemma. We present computational results on real-world instances and compare the new approach with the well-established traffic assignment model. The essence of this study is that system-optimal routing of traffic flow with explicit integration of user constraints leads to a better performance than the user equilibrium, while simultaneously guaranteeing superior fairness compared to the pure system optimum.

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System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion

We present a short geometric proof for the price of anarchy results that have recently been established in a series of papers on selfish routing in multicommodity flow networks. This novel proof also facilitates two new types of results: On the one hand, we give pseudo-approximation results that depend on the class of allowable cost functions. On the other hand, we derive improved bounds on the inefficiency of Nash equilibria for situations in which the equilibrium travel times are within reasonable limits of the free-flow travel times. These tighter bounds help to explain empirical observations in vehicular traffic networks. Our analysis holds in the more general context of congestion games, which provides the framework in which we describe this work.

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On the inefficiency of equilibria in congestion games

This paper develops a game theoretic model based on a two-sided market framework to investigate the net neutrality debate. In particular, we consider investment incentives of Internet Service Providers (ISPs) under a neutral and non-neutral network regimes. In our model, two interconnected ISPs compete over quality and prices for heterogeneous content providers (CPs) and heterogeneous consumers. We consider two definitions of a non-neutral network: in the first, ISPs charge access fees to off-network CPs; in the second, ISPs offer "priority lanes''. In the neutral regime, connecting to a single ISP allows a CP to communicate with all consumers and all CPs obtain the same quality of service. With a combination of theoretical and numerical results we find that under both definitions ISPs' quality-investment levels are driven by the trade-off they make between softening price competition on the consumer side and increasing revenues extracted from CPs. Specifically, in the non-neutral regime, because it is easier to extract surplus through appropriate CP pricing, ISPs' investment levels are larger. Because CP quality is enhanced by the quality of ISPs, larger investment levels imply that CPs' revenues increase. Similarly, consumer surplus increases as well. The main insight resulting from our model is that social welfare is larger in the non-neutral regime. Our results highlight important mechanisms related to ISPs' investments that play a key role in market outcomes, providing useful insights that enrich the net neutrality debate.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID2168893_code336339.pdf?abstractid=1641359&mirid=1&type=2

Investment in Two Sided Markets and the Net Neutrality Debate

In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines.

Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria.

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Nicolas E. Stier-Moses

Papers

Selfish Routing in Capacitated Networks

System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion

On the inefficiency of equilibria in congestion games

Investment in Two Sided Markets and the Net Neutrality Debate

The Impact of Oligopolistic Competition in Networks