The Price of Fairness

In this paper we study resource allocation problems that involve multiple self-interested parties or players and a central decision maker. We introduce and study the price of fairness, which is the relative system efficiency loss under a “fair” allocation assuming that a fully efficient allocation is one that maximizes the sum of player utilities. We focus on two well-accepted, axiomatically justified notions of fairness, viz., proportional fairness and max-min fairness. For these notions we provide a tight characterization of the price of fairness for a broad family of problems.National Science Foundation (U.S.) (grant DMI- 0556106)National Science Foundation (U.S.) (grant EFRI-0735905

The Impact of Stackelberg Routing in General Networks

We investigate the impact of Stackelberg routing in network routing games. In this setting, a fraction alpha of the entire demand is first routed by a central authority, called the Stackelberg leader, while the remaining demand is then routed by selfish (nonatomic) players. The aim is to devise Stackelberg strategies, i.e., strategies to route the centrally controlled demand, so as to minimize the price of anarchy of the resulting flow. Although several advances have been made recently in proving that Stackelberg routing may in fact significantly reduce the price of anarchy for certain network topologies, it is still an open question whether this holds true in general. We answer this question negatively. We prove that the price of anarchy achievable via Stackelberg routing can be unbounded even for single-commodity networks. In light of this negative result, we consider bicriteria bounds. We develop an efficiently computable Stackelberg strategy that induces a flow whose cost is at most the cost of an optimal flow with respect to demands scaled by a factor of 1 + (1-alpha)^1/2. Thus, we obtain a smooth trade-off curve that scales between the absence of centralized control (doubling the demands is sufficient) and completely centralized control (no scaling is necessary). Finally, we analyze the effectiveness of a simple Stackelberg strategy, called SCALE, for polynomial latency functions. Our analysis is based on a general technique which is simple, yet powerful enough to obtain (almost) tight bounds for SCALE in general networks. For linear latency functions, we derive an upper bound that matches the current best one and show that this bound is tight. For general polynomial latency functions, we obtain upper bounds that improve all previously known ones

The Price of Anarchy and Computation of Equilibria in Non-atomic Consumption-Relevance Congestion Games

We present an extension to the model of non-atomic congestion games (NCG). NCGs enforce a symmetry between the consumption of elements (e.g., network links) and their relevance for the players: players utilizing an element e through a strategy S (e.g., a multicast tree) with rate of consumption C_{eS}>0 experience the element's latency amplified by that same factor C_{eS}. Our extension instead allows a factor R_{eS}, independent of C_{eS}, to express the amplification of the element's latency from the players' perspective, or, in other words, the relevance of element e for strategy S. We therefore call the extended model non-atomic consumption-relevance congestion games (NCRCG). NCRCGs exhibit new phenomena, including multiple Nash equilibria of different social cost and -- even from a worst-case point of view -- a dependence of the price of anarchy on structural parameters not limited to the class of element latency functions used. It poses new computational challenges. We prove almost tight lower, upper, and bicriteria bounds for the price of anarchy for super-homogeneous classes of element latency functions. We show a positive computational result for affine element latency functions. A summary of experimental results is given, which suggest that our lower bound is the best possible

Experimental Studies of the Price of Anarchy in Non-atomic Consumption-Relevance Congestion Games

The model of non-atomic consumption-relevance congestion games (NCRCG) is an extension of the well-known non-atomic congestion games (NCG). We introduced the NCRCG model in a previous report (0814) and proved worst-case lower and upper bounds on the price of anarchy. These bounds are are tight up to a factor of gamma, where gamma is a new structural parameter of the game; we have gamma=1 for NCGs. This experimental work substantiates our conjecture that the worst-case lower bound is the best possible, i.e., that it actually also is an upper bound

Price of anarchy for reliability-based traffic assignment and network design

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Application of robust and inverse optimization in transportation

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 79-82).We study the use of inverse and robust optimization to address two problems in transportation: finding the travel times and designing a transportation network. We assume that users choose the route selfishly and the flow will eventually reach an equilibrium state (User Equilibrium). The first part of the thesis demonstrates how inverse and robust optimization can be used to find the actual travel times given a stable flow on the network and some noisy information on travel times from different users. We model the users' perception of travel times using three different sets and solve the robust inverse problem for all of them. We also extend the idea to find parametric functional forms for travel times given historical data. Our numerical results illustrate the significant improvement obtained by our models over a simple fitting model. The second part of the thesis considers the network design problem under demand uncertainty. We show that for affine travel time functions, the deterministic problem can be formulated as a mixed integer programming problem with quadratic objective and linear constraints. For the robust network design problem, we propose a decomposition scheme: breaking a tri-level programming problem into two smaller problems and re-iterating until a good solution is obtained. To deal with the expensive computation required by large networks, we also propose a heuristic robust simulated annealing approach. The heuristic algorithm is computationally tractable and provides some encouragingly results in our simulations.by Thai Dung Nguyen.S.M

Demand Management in Decentralized Logistics Systems and Supply Chains

We analyze issues arising from demand management in decentralized decision-making environments. We consider logistics systems and supply chains, where companies' operations are handled with independent entities whose decisions affect the performance of the overall system. In the first study, we focus on a logistics system in the sea cargo industry, where demand is booked by independent sales agents, and the agents' capacity limits and sales incentives are determined by a central headquarters. We develop models for the central headquarters to analyze and optimize capacity allocation and sales incentives to improve the performance of the decentralized system. We use network flow problems to incorporate agent behavior in our models, and we link these individual problems through an overall optimization problem that determines the capacity limits. We prove a worst-case bound on the decentralized system performance and show that the choice of sales incentive impacts the performance. In the second study, we focus on supply chains in the automotive industry, where decentralization occurs as a result of the non-direct sales channels of the auto manufacturers. Auto manufacturers can affect their demand through sales promotions. We use a game theoretical model to examine the impact of retailer incentive and customer rebate promotions on the manufacturer's pricing and the retailer's ordering/sales decisions. We consider several models with different demand characteristics and information asymmetry between the manufacturer and a price discriminating retailer. We characterize the subgame-perfect Nash equilibrium decisions and determine which promotion would benefit the manufacturer under which market conditions. We find that the retailer incentives are preferred when demand is known. On the other hand, when demand is highly uncertain the manufacturer is better off with customer rebates. We extend this research by analyzing a competitive setting with two manufacturers and two retailers, where the manufacturers' promotions vary between retailer incentives and customer rebates. We find an equilibrium outcome where customer rebates reduce the competitor's profits to zero. We observe in numerical examples that the manufacturers are able to increase their sales and profits with retailer incentives, although this can be at the expense of the retailers' profits under some situations.Ph.D.Committee Chair: Swann, Julie; Committee Member: Ergun, Ozlem; Committee Member: Ferguson, Mark; Committee Member: Griffin, Paul; Committee Member: Keskinocak, Pina

Netzwerke und verteilte Operation: Der Preis der Anarchie in nicht-atomarem Routing und Netzwerkformierung

The price of anarchy is a measure for performance loss due to individuals operating in a distributed manner, i.e., without or with only limited central control or without or with only limited cooperation. In the first part, a network is given and used in a distributed manner, namely for multicast routing, i.e., each sender wishes to transmit a message to multiple receivers simultaneously. We prove almost tight upper and lower bounds on the price of anarchy and conduct an experimental study. In the second part, a network is formed. Each vertex of the (to-be-built) network may invest in the building of links. The formation takes place under the knowledge that an adversary will later delete exactly one link. Vertices wish to maintain good connectivity. We prove tight upper and lower bounds on the price of anarchy for two different adversaries.Der Preis der Anarchie ist ein Maß für den Leistungsverlust dadurch, dass Individuen in verteilter Weise operieren, d.h. dass sie nicht oder nur eingeschränkt koordiniert werden oder nicht oder nur eingeschränkt kooperieren. Im ersten Teil wird ein gegebenes Netzwerk in verteilter Weise genutzt, und zwar für Multicast-Routing, d.h. es möchte jeder Sender eine Mehrzahl Empfänger gleichzeitig erreichen. Wir beweisen nahezu scharfe obere und untere Schranken für den Preis der Anarchie und führen eine experimentelle Studie durch. Im zweiten Teil geht es um die Formierung von Netzwerken. Jeder Knoten des (zu formierenden) Netzwerkes hat die Wahl, in Verbindungen zu investieren. Bei uns findet die Netzwerkformierung unter dem Wissen statt, dass später genau eine Verbindung durch einen Gegner zerstört werden wird. Die Knoten streben an, trotzdem gut verbunden zu bleiben. Wir beweisen scharfe obere und obere Schranken für den Preis der Anarchie für zwei verschiedene Formen von Gegnern