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## Worst-case equilibria (1999)

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Venue: | IN PROCEEDINGS OF THE 16TH ANNUAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE |

Citations: | 847 - 17 self |

### Citations

961 | Factoring polynomials with rational coefficients, Mathematische Annalen 261 - Lenstra, Lenstra, et al. - 1982 |

662 | Algorithmic mechanism design - Nisan, Ronen - 2001 |

657 | How bad is selfish routing?
- Roughgarden, Tardos
- 2002
(Show Context)
Citation Context ...refer the reader to the book [14] which devotes a significant fraction to these issues. The popularity of the concept of the price of anarchy owes much to the follow-up work of Roughgarden and Tardos =-=[18]-=- which opened the way to studying the price of anarchy in atomic and nonatomic congestion games. The conference version of this work together with the work of Nisan and Ronen [13, 12] on algorithmic m... |

654 | Existence of Equilibrium for a Competitive Economy,” - Arrow, Debreu - 1954 |

591 | Algorithmic Game Theory
- Nisan, Roughgarden, et al.
- 2007
(Show Context)
Citation Context ...du 1 The conference version of this work [9] appeared a decade ago and it has been followed by a large amount of work on the concept of the price of anarchy (as witnessed by the extensive coverage in =-=[14]-=-). In this journal version we tried to keep as much as possible the text of the original paper. There are, though, important changes because results that were substantially improved in the meantime ar... |

334 |
and the internet”;. In
- Papadimitriou, “Algorithms
- 2001
(Show Context)
Citation Context ...rm “price of anarchy” instead of the original term “coordination ratio”. The use of the latter term faded away in the literature, replaced by the term “price of anarchy” which was first introduced in =-=[16]-=-. 1which are more resilient to video-like traffic. Their point of view is also that of the mechanism design aspect of game theory, in that they try to design games (strategy spaces and reward tables)... |

318 | Integer programming with a fixed number of variables. - Lenstra - 1983 |

218 | Making greed work in networks: a game-theoretic analysis of switch service disciplines
- Shenker
- 1994
(Show Context)
Citation Context ..., with the Prisoner's Dilemma [8, 10] being the best-known example. Conditions under which Nash equilibria can achieve or approximate the overall optimum have been studied extensively ([10]� see also =-=[5, 7, 11]-=- for studies on networks). However, this line of previous work compares the overall optimum with the best Nash equilibrium, not the worst, as be ts our line of reasoning. To put it otherwise, this pre... |

172 | Tight bounds for worst-case equilibria. In
- Czumaj, Vocking
- 2002
(Show Context)
Citation Context ...links, log m the price of anarchy is Ω( log log m ) (Theorem 1). In the conference version of the paper we had a nonmatching upper bound. It was later shown that this lower bound is essentially tight =-=[3, 8]-=-. 2 All Nash equilibria We consider the case of n agents sharing m identical links. Before describing all Nash equilibria, we need a few definitions. We usually use subscripts for agents and superscri... |

147 | Router Mechanisms to Support End-to-End Congestion Control, Technical report, Network Research Group at LBNL
- Floyd, Fall
- 1997
(Show Context)
Citation Context ...link and P wi its load [7]. More important is the study of realistic Internet metrics, that result from the employed protocols such as the one related to TCP and the square root of the drop frequency =-=[3]-=-. Finally, it would be extremely interesting, once the relative quality of the Nash equilibria in such situations is better understood, to employ suchunderstanding in the design of improved protocols ... |

139 | Architecting noncooperative networks
- Korilis, Lazar, et al.
- 1995
(Show Context)
Citation Context ...e sum of all delays over all agents, say. The question we want to ask is, how far from the optimum total delay can be the total delay achieved by a Nash equilibrium? Numerical experiments reported in =-=[6]-=- imply that there are Nash equilibria which can be more than 20% o the overall optimum. In this paper we address a very simple special case of this problem, in which the network is just a set of m par... |

103 | Factoring Polynomials with Rational Coe#- cients - Lenstra, Lenstra - 1982 |

100 | Complementary pivot theory of mathematical programming. Linear Algebra and its Applications, - Cottle, Dantzig - 1968 |

90 |
Game Theory (3rd ed.).
- Owen
- 1995
(Show Context)
Citation Context ...orithmic and combinatorial questions and results. It is nontrivial to arrive at a compelling mathematical formulation of this question. Independent, non-cooperative agents obviously evoke game theory =-=[8]-=-, and its main concept of rational behavior, the Nash equilibrium: In an environment inwhicheachagentisaware of the situation facing all other agents, a Nash equilibrium is a combination of choices (d... |

77 | On the existence of equilibria in noncooperative optimal flow control
- Korilis, Lazar
- 1995
(Show Context)
Citation Context ... with the Prisoner 's Dilemma [8, 10] being the best-known example. Conditions under which Nash equilibria can achieve or approximate the overall optimum have been studied extensively ([10]; see also =-=[5, 7, 11]-=- for studies on networks). However, this line of previous work compares the overall optimum with the best Nash equilibrium, not the worst, as befits our line of reasoning. To put it otherwise, this pr... |

59 | P.G.: Approximate Equilibria and Ball Fusion
- Koutsoupias, Mavronicolas, et al.
- 2003
(Show Context)
Citation Context ...links, log m the price of anarchy is Ω( log log m ) (Theorem 1). In the conference version of the paper we had a nonmatching upper bound. It was later shown that this lower bound is essentially tight =-=[3, 8]-=-. 2 All Nash equilibria We consider the case of n agents sharing m identical links. Before describing all Nash equilibria, we need a few definitions. We usually use subscripts for agents and superscri... |

55 |
On complexity as bounded rationality
- Papadimitriou, Yannakakis
- 1994
(Show Context)
Citation Context ...istic or randomized), one for each agent, from whichnoagent has an incentive to unilaterally moveaway.Nash equilibria are known not to always optimize overall performance, with the Prisoner's Dilemma =-=[8, 10]-=- being the best-known example. Conditions under which Nash equilibria can achieve or approximate the overall optimum have been studied extensively ([10]� see also [5, 7, 11] for studies on networks). ... |

47 | Quality of service provision in noncooperative networks: heterogeneous preferences, multi-dimensional QoS vectors, and burstiness
- Park, Sitharam, et al.
- 1998
(Show Context)
Citation Context ...robabilities p 1 i of the stochastic agents (p2 i =1; p1 i ). p 1 s2 i = ; s1 + s2 (s2 ; s1) P i wi +(s2d1 ; s1d2 ) (k ; 1)(s1 + s2)wi It is not hard to verify that these probabilities indeed satisfy =-=(9)-=-. To prove the theorem, we consider the case of no initial loads and two agents with jobs w1 = s2 and w2 = s1. The probabilities are p1 1 = s 2 1 s2(s1+s2) and p12 =1; s 2 2 .We can s1(s1+s2) then com... |

40 |
Bounds for list schedules on uniform processors,
- Cho, Sahni
- 1980
(Show Context)
Citation Context ... easy to see that M j = L j + X i p j i wi: (1)sFrom the point of view of agent i, its nish time when its own tra c wi is assigned to link j is c j i = wi + L j + X i6=t p j twt = M j +(1; p j i )wi: =-=(2)-=- Probabilities p j de ne a Nash equilibrium if there is no incentive for agent i to i change its strategy. Thus, agent i will assign nonzero probabilities only to links j that minimize c j i .We will ... |

38 | Algorithms for Selfish Agents: Mechanism Design for Distributed Computation,” - Nisan - 1999 |

36 | Equilibrium in a discrete exchange economy with money - Gale - 1984 |

27 | The Computation of Economic Equilibria, with Collaboration of - Scarf - 1973 |

26 | Optimal routing control: game theoretic approach
- La, Anantharam
- 1997
(Show Context)
Citation Context ..., with the Prisoner's Dilemma [8, 10] being the best-known example. Conditions under which Nash equilibria can achieve or approximate the overall optimum have been studied extensively ([10]� see also =-=[5, 7, 11]-=- for studies on networks). However, this line of previous work compares the overall optimum with the best Nash equilibrium, not the worst, as be ts our line of reasoning. To put it otherwise, this pre... |

13 | Integer programming with a number of variables - Lenstra - 1983 |

11 | Communication Complexity of Combinatorial Auctions”, manuscript - Nisan - 2001 |

7 | Papadimitriou: On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence - H - 1994 |

6 | M.: On the approximability of trade-o↵s and optimal access of web sources - Papadimitriou, Yannakakis - 2000 |

5 |
On the existence of equilibria in noncooperative optimal ow control
- Korilis, Lazar
- 1995
(Show Context)
Citation Context ..., with the Prisoner's Dilemma [8, 10] being the best-known example. Conditions under which Nash equilibria can achieve or approximate the overall optimum have been studied extensively ([10]� see also =-=[5, 7, 11]-=- for studies on networks). However, this line of previous work compares the overall optimum with the best Nash equilibrium, not the worst, as be ts our line of reasoning. To put it otherwise, this pre... |

5 | Papadimitriou," "Algorithms, games, and the internet - H - 2001 |

3 | Algebraic Cell Decomposition in NC (Preliminary Version - Kozen, Yap - 1985 |

3 | The Communication Complexity of Ecient Allocation Problems" presented - Nisan, Segal - 2001 |

2 | The Competitive Mechanism is Dimensionally Efficient Uniquely - Jordan - 1982 |

2 | On Information Decentralization and Efficiency in Resourse Allocation Mechanism - Hurwicz - 1986 |

1 | The Competitive Mechanism is Dimensionally Ecient Uniquely - Jordan - 1982 |

1 | On Information Decentralization and Eciency in Resourse Allocation Mechanism - Hurwicz - 1986 |

1 | the Internet" STOC 2001 [12] C. Papadimitriou, "The Complexity of the Parity Argument and other Inefficient Proofs of Existence - Papadimitriou, Algorithms - 1994 |

1 | Yannakakis "The complexity of tradeoffs, and optimal access of web sources", FOCS - Papadimitriou, M - 2000 |