A class of games possessing pure-strategy Nash equilibria
TL;DR: In this paper, a class of noncooperative games (of interest in certain applications) is described and each game in the class is shown to possess at least one Nash equilibrium in pure strategies.
Abstract: A class of noncooperative games (of interest in certain applications) is described Each game in the class is shown to possess at least one Nash equilibrium in pure strategies
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15 Dec 2008TL;DR: 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 multi agent systems, while integrating ideas from operations research, game theory, economics, logic, and even philosophy and linguistics.
Abstract: 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.
2,068 citations
Cites background from "A class of games possessing pure-st..."
...It was already me ntioned in Chapter 3 that extensive-form games were discussed explicitly in von Neumann and Morgenstern [1944], as was backward induction. Subgame perfectio n was introduced by Selten [1965], who received a Nobel Prize in 1994....
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...It was already me ntioned in Chapter 3 that extensive-form games were discussed explicitly in von Neumann and Morgenstern [1944], as was backward induction....
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Book•
01 Jan 2007TL;DR: A new era of theoretical computer science addresses fundamental problems about auctions, networks, and human behavior in a bid to solve the challenges of 21st Century finance.
Abstract: A new era of theoretical computer science addresses fundamental problems about auctions, networks, and human behavior.
1,994 citations
TL;DR: The degradation in network performance due to unregulated traffic is quantified and it is proved that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency.
Abstract: We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times---the total latency---is minimized.In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimum-latency path available to it, given the network congestion caused by the other users. In general such a "selfishly motivated" assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance.In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total latency of the routes chosen by unregulated selfish network users may be arbitrarily larger than the minimum possible total latency; however, we prove that it is no more than the total latency incurred by optimally routing twice as much traffic.
1,703 citations
Cites background from "A class of games possessing pure-st..."
...Dafermos and Sparrow [7] were perhaps the first authors interested in computing the equilibrium efficiently, and many subsequent papers gave increasingly efficient methods for computing equilibria (see [10] for a survey); others have extended these results to more sophisticated models (see for example [1, 6, 10, 13, 21, 22, 27, 29, 30])....
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Book•
01 Jan 2005TL;DR: A survey of recent work that analyzes the price of anarchy of selfish routing, a classical mathematical model of how self-interested users might route traffic through a congested network.
Abstract: 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.
952 citations
Cites methods from "A class of games possessing pure-st..."
...Led by the work of Rosenthal [62] and Monderer and Shapley [49], potential functions have become a standard tool in noncooperative game theory for proving the existence of pure-strategy Nash equilibria in certain classes of games....
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12 Nov 2000
TL;DR: It is proved that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed).
Abstract: We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times-the total latency-is minimized. In many settings, including the Internet and other large-scale communication networks, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimum-latency path available to it, given the network congestion caused by the other users. In general such a "selfishly motivated" assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance. We quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and non-decreasing in the edge congestion.
811 citations
References
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01 Jan 1961TL;DR: In place of a survey or evaluation of industrial studies, two broad issues which are relevant to all such applications will be discussed, including the use of linear programming models as guides to data collection and analysis and prognosis of fruitful areas of additional research, especially those which appear to have been opened by industrial applications.
Abstract: An accelerating increase in linear programming applications to industrial problems has made it virtually impossible to keep abreast of them, not only because of their number and diversity but also because of the conditions under which many are carried out. Industrial and governmental secrecy is often present. Other conditions also bar access to ascertainment and assessment of the pattern of applications. Lack of a tradition for publication is one. Failure to ascertain the general significance of particular findings is another, as is discouragement arising from the fact that similar applications have previously been published by others. Immediate remedies are not available for these difficulties. Presumably conventions such as this will help, over a period of time, by encouraging informal contacts between interested persons.
A talk on “industrial applications of linear programming” must be altered to suit these circumstances. In place of a survey or evaluation of industrial studies, two broad issues which are relevant to all such applications will be discussed. These are, 1 use of linear programming models as guides to data collection and 2 analysis and prognosis of fruitful areas of additional research, especially those which appear to have been opened by industrial applications.
1,763 citations
Additional excerpts
...See [CHARNES and COOPER, 1961], for example....
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673 citations
TL;DR: It is shown that pure-strategy Nash equilibria exist and that any solution to an integer-variable analogue of the usual network equilibrium model is such a Nash equilibrium.
Abstract: In the usual approach to network equilibrium models, the flow variables are modeled as continuous. When the problem under study involves discrete decision makers each controlling an indivisible unit of flow, another approach is called for. We treat the problem as an n-person noncooperative game with pure strategies corresponding to feasible paths through the network. It is shown that pure-strategy Nash equilibria exist and that any solution to an integer-variable analogue of the usual network equilibrium model is such a Nash equilibrium. It is also shown that when individuals can control more than a single unit of flow and want to minimize the sum of their costs, pure-strategy Nash equilibria do not necessarily exist.
155 citations