## Coordination mechanisms (2004)

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Venue: | PROCEEDINGS OF THE 31ST INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING, IN: LECTURE NOTES IN COMPUTER SCIENCE |

Citations: | 43 - 5 self |

### BibTeX

@INPROCEEDINGS{Christodoulou04coordinationmechanisms,

author = {George Christodoulou and Elias Koutsoupias and Akash Nanavati},

title = {Coordination mechanisms },

booktitle = {PROCEEDINGS OF THE 31ST INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING, IN: LECTURE NOTES IN COMPUTER SCIENCE},

year = {2004},

pages = {345--357},

publisher = {Springer}

}

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### Abstract

We introduce the notion of coordination mechanisms to improve the performance in systems with independent selfish and non-colluding agents. The quality of a coordination mechanism is measured by its price of anarchy—the worst-case performance of a Nash equilibrium over the (centrally controlled) social optimum. We give upper and lower bounds for the price of anarchy for selfish task allocation and congestion games.

### Citations

1960 | A course in game theory
- Osborne, Rubinstein
- 1994
(Show Context)
Citation Context ...l version). 1.2 Related work Mechanisms to improve coordination of selfish agents is not a new idea and we only mention here work that directly relates to our approach. A central topic in game theory =-=[17]-=- is the notion of mechanism design in which the players are paid (or penalized) to “coordinate”. The differences between mechanism design and the coordination mechanism model are numerous. The most st... |

1409 |
Counterspeculation, Auctions and Competitive Sealed Tenders
- Vickrey
- 1961
(Show Context)
Citation Context ...ill discuss soon, the answer to the first question is positive and to the second question negative. There are few mechanisms that are known to be truthful and the beststudied one is the VCG mechanism =-=[31, 8, 12]-=-. Example 4. The VCG mechanism and affine maximizers The VCG mechanism implements the social choice function of selecting the outcome (column) with the maximum total value: f(v) = argmax j∈{1,...,k} n... |

1192 |
Optimal Auction Design
- Myerson
- 1981
(Show Context)
Citation Context ...each player has only one real private value and his objective is proportional to this value (for a precise definition see Chapters 9 and 12 of [26]). Such problems were studied extensively by Myerson =-=[25]-=-. Furthermore, the optimal allocation is monotone and therefore truthful, but it cannot be computed in polynomial time unless P=NP. It is therefore an appropriate example to explore the interplay betw... |

685 | Worst-case equilibria
- Koutsoupias, Papadimitriou
- 1999
(Show Context)
Citation Context ...uilibrium over the (centrally controlled) social optimum. We give upper and lower bounds for the price of anarchy for selfish task allocation and congestion games. 1 Introduction The price of anarchy =-=[11, 18]-=- measures the deterioration in performance of systems on which resources are allocated by selfish agents. It captures the lack of coordination between independent selfish agents as opposed to the lack... |

647 |
Incentives in teams
- Groves
- 1973
(Show Context)
Citation Context ...ill discuss soon, the answer to the first question is positive and to the second question negative. There are few mechanisms that are known to be truthful and the beststudied one is the VCG mechanism =-=[31, 8, 12]-=-. Example 4. The VCG mechanism and affine maximizers The VCG mechanism implements the social choice function of selecting the outcome (column) with the maximum total value: f(v) = argmax j∈{1,...,k} n... |

608 |
Approximation algorithms for NP-hard problems
- Hochbaum
- 1997
(Show Context)
Citation Context ...opments on this important problem in Algorithmic Game Theory. We treat both the related and the unrelated version of the problem. 1 The scheduling problem The problem of scheduling unrelated machines =-=[21, 14]-=- is one of the most fundamental algorithmic problems: There are n machines and m tasks∗ and machine i can execute task j in time tij . These times can be totally unrelated (thus the name of the proble... |

582 | Algorithmic mechanism design
- Nisan, Ronen
- 2001
(Show Context)
Citation Context ...ism is a way to introduce traffic lights. Also, the algorithmic and communication issues involved in mechanism design seem to be completely different than the ones involved in coordination mechanisms =-=[16, 15, 19, 1]-=-. The idea of designing games to improve coordination appears also in the work of Korilis, Lazar, and Orda [9] but there the goal is to design games with a unique Nash equilibrium; there is no attempt... |

564 | How bad is selfish routing
- Roughgarden, Tardos
- 2002
(Show Context)
Citation Context ...te (original) optimum which is independent of our choice of scheduling policies. As a second example, consider the selfish routing problem whose price of anarchy was studied by Roughgarden and Tardos =-=[23]-=-. In a network in which the latency experienced by the traffic on an edge depends on the traffic traversing the edge, selfish users route traffic on minimum-latency paths. The price of anarchy can be ... |

548 |
Some theoretical aspects of road traffic research
- Wardrop
- 1952
(Show Context)
Citation Context ...e). Of special interest is the symmetric case of infinitely many players. Particularly, we will consider the coordination model for routing which is based on the well-studied routing model of Wardrop =-=[18, 16]-=-. In this routing model, the set of facilities is the set of edges of a finite network, the set of strategies for a player i is the set of paths from a source si to a destination ti, and the cost (del... |

449 |
W.: A class of games possessing pure-strategy Nash equilibrium
- Rosenthal
- 1973
(Show Context)
Citation Context ...given total flow. This can be also cast as a special case of coordination mechanisms that allow either a given specific delay function or infinity (and fixed total flow).s2 The Model Congestion games =-=[20, 13, 6]-=-, introduced by Rosenthal, is an important class of games that capture many aspects of selfish behavior in networks. A congestion game is defined by a tuple (N, M, (Σi)i∈N , (c j )j∈M ) where N is the... |

402 |
L.S.: Potential games
- Monderer, Shapley
- 1996
(Show Context)
Citation Context ...ers is fixed. There are interesting questions when we assume that the number of players is not fixed in advance, but we do not treat them in this work. Our second example is based on congestion games =-=[35, 28]-=-. To simplify the discussion let’s consider the special class of single-commodity (that is, symmetric) congestion games in this section. In a single-commodity congestion game there are n selfish playe... |

350 | Algorithmic Game Theory
- Nisan, Roughgarden, et al.
- 2007
(Show Context)
Citation Context ...t’s a typical single-parameter problem, which means that each player has only one real private value and his objective is proportional to this value (for a precise definition see Chapters 9 and 12 of =-=[26]-=-). Such problems were studied extensively by Myerson [25]. Furthermore, the optimal allocation is monotone and therefore truthful, but it cannot be computed in polynomial time unless P=NP. It is there... |

343 |
Bounds for certain multiprocessing anomalies
- Graham
- 1966
(Show Context)
Citation Context ...e smaller loads. In turn this is true for each load. Notice however that this is exactly the greedy scheduling with the loads ordered in decreasing size. It has been analyzed in Graham’s seminal work =-=[8]-=- where it was established that its approximation ratio is 4/3 − 1/(3m). Given that the total delay introduced by the δ terms increases the social cost by at most a factor of δ, we conclude that the pr... |

300 |
the Internet
- Papadimitriou, “Algorithms
- 2001
(Show Context)
Citation Context ...uilibrium over the (centrally controlled) social optimum. We give upper and lower bounds for the price of anarchy for selfish task allocation and congestion games. 1 Introduction The price of anarchy =-=[11, 18]-=- measures the deterioration in performance of systems on which resources are allocated by selfish agents. It captures the lack of coordination between independent selfish agents as opposed to the lack... |

218 | Approximation algorithms for scheduling unrelated parallel machines
- Lenstra, Shmoys, et al.
- 1987
(Show Context)
Citation Context ...opments on this important problem in Algorithmic Game Theory. We treat both the related and the unrelated version of the problem. 1 The scheduling problem The problem of scheduling unrelated machines =-=[21, 14]-=- is one of the most fundamental algorithmic problems: There are n machines and m tasks∗ and machine i can execute task j in time tij . These times can be totally unrelated (thus the name of the proble... |

189 | The price of anarchy is independent of the network topology
- Roughgarden
(Show Context)
Citation Context ... coordination mechanism with price of anarchy approximately 1.19. This special case network played a special role in the study of anarchy for the selfish routing problem. Essentially, it was shown in =-=[15]-=- that the problem of larger networks can be reduced to this case. If the same holds for coordination mechanisms, then the above theorem will be central in resolving the general case too. 5 Open proble... |

171 | Tight bounds for worst-case equilibria
- Czumaj, Vöcking
- 2002
(Show Context)
Citation Context ...ulting allocation may be suboptimal. The price of anarchy, that is, the worst-case ratio of the maximum latency at a Nash equilibrium over the optimal allocation can be as high as Θ(log m/ log log m) =-=[11, 5, 10]-=-. The question is “How can we improve ⋆ Research supported in part by the IST (FLAGS, IST-2001-33116) program and by NSF.sthe price of anarchy?”; and what mechanisms one can use to improve the overall... |

162 |
Congestion games with player-specific payoff functions
- Milchtaich
- 1996
(Show Context)
Citation Context ...ze congestion games in two directions: First, to allow the players to have loads or weights and second, to allow asymmetric cost functions where players experience different cost for using a facility =-=[27, 17]-=-. These generalizations are realized by cost functions c j i , one for each player —the cost of player i for using facility j is now c j i (wj) where wj is the sum of weights of the players using faci... |

141 | The price of anarchy of finite congestion games
- Christodoulou, Koutsoupias
- 2005
(Show Context)
Citation Context ...relation between the potential and the social cost of a set of strategies; based on these, we give a coordination mechanism with price of anarchy n for series-parallel network congestion games. 1 See =-=[4, 10, 9, 1]-=- for results on price of anarchy of congestion games for linear and polynomial latency functions. In this work, we consider general latencies.1.2 Related work Mechanisms to improve coordination of se... |

130 | Architecting noncooperative networks
- Korilis, Lazar, et al.
- 1995
(Show Context)
Citation Context ... to be completely different than the ones involved in coordination mechanisms [16, 15, 19, 1]. The idea of designing games to improve coordination appears also in the work of Korilis, Lazar, and Orda =-=[9]-=- but there the goal is to design games with a unique Nash equilibrium; there is no attempt to compare it with the potential optimum. In an attempt to reduce total delay at Nash equilibrium in the self... |

120 | The price of routing unsplittable flow
- Awerbuch, Azar, et al.
- 2005
(Show Context)
Citation Context ...relation between the potential and the social cost of a set of strategies; based on these, we give a coordination mechanism with price of anarchy n for series-parallel network congestion games. 1 See =-=[4, 10, 9, 1]-=- for results on price of anarchy of congestion games for linear and polynomial latency functions. In this work, we consider general latencies.1.2 Related work Mechanisms to improve coordination of se... |

111 | Frugal path mechanisms
- Archer, Tardos
(Show Context)
Citation Context ...ism is a way to introduce traffic lights. Also, the algorithmic and communication issues involved in mechanism design seem to be completely different than the ones involved in coordination mechanisms =-=[16, 15, 19, 1]-=-. The idea of designing games to improve coordination appears also in the work of Korilis, Lazar, and Orda [9] but there the goal is to design games with a unique Nash equilibrium; there is no attempt... |

107 | Settling the complexity of two-player Nash equilibrium
- Chen, Deng
- 2006
(Show Context)
Citation Context ...on mechanism: there is a unique Nash equilibrium (thus it is easy for players to “agree”) and it has low computational complexity. In contrast, computing Nash equilibria is potentially a hard problem =-=[7]-=-. The above theorem shows that good coordination mechanisms reduce the price of anarchy from Θ(log m/log log m) to a small constant. Is there a coordination mechanism with better price of anarchy than... |

100 | Pricing Network Edges for Heterogeneous Selfish Users
- Cole, Dodis, et al.
- 2003
(Show Context)
Citation Context ... The most straightforward comparison can be exhibited in the selfish routing problem: both aim at improving coordination, but mechanism design can be seen as a way to introduce tolls (see for example =-=[2, 3]-=-), while coordination mechanism is a way to introduce traffic lights. Also, the algorithmic and communication issues involved in mechanism design seem to be completely different than the ones involved... |

98 |
Bounds for certain multiprocessor anomalies
- Graham
- 1966
(Show Context)
Citation Context ...urn this is true for each load. Notice however that this is exactly the greedy scheduling with the loads ordered in decreasing size (aka LPT scheduling). It has been analyzed in Graham’s seminal work =-=[18]-=- where it was established that its approximation ratio is 4/3 − 1/(3m). Given that the total delay introduced by the δ terms increases the social cost by at most δ, we conclude that the price of anarc... |

89 |
A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach
- Hochbaum, Shmoys
- 1988
(Show Context)
Citation Context ...reals instead of integers, we call this the fractional scheduling problem. The computational complexity of these problems is completely settled: There is a polynomial time approximation scheme (PTAS) =-=[13]-=- for the related machines problem and a fully-PTAS (FPTAS) [15] when the number of machines is fixed; the general case is strongly NP-complete, so we don’t expect to find an FPTAS unless P=NP. For the... |

89 |
Exact and approximate algorithms for scheduling nonidentical processors
- Horowitz, Sahni
- 1976
(Show Context)
Citation Context ...ng problem. The computational complexity of these problems is completely settled: There is a polynomial time approximation scheme (PTAS) [13] for the related machines problem and a fully-PTAS (FPTAS) =-=[15]-=- when the number of machines is fixed; the general case is strongly NP-complete, so we don’t expect to find an FPTAS unless P=NP. For the fractional version of the problem, there is a polynomial-time ... |

86 | A necessary and sufficient condition for rationalizability in a quasi-linear context - Rochet - 1987 |

76 |
Algorithmic mechanism design (extended abstract
- Nisan, Ronen
- 1999
(Show Context)
Citation Context ... to find an FPTAS unless P=NP. For the fractional version of the problem, there is a polynomial-time algorithm (because it can be expressed as a linear program). Nisan and Ronen in their seminal work =-=[27, 28]-=- which started the area of Algorithmic Mechanism Design considered the unrelated machines problem from a game-theoretic point of view: suppose that each machine i is a rational agent who is the only o... |

68 | How much can taxes help selfish routing
- Cole, Dodis, et al.
- 2006
(Show Context)
Citation Context ... The most straightforward comparison can be exhibited in the selfish routing problem: both aim at improving coordination, but mechanism design can be seen as a way to introduce tolls (see for example =-=[2, 3]-=-), while coordination mechanism is a way to introduce traffic lights. Also, the algorithmic and communication issues involved in mechanism design seem to be completely different than the ones involved... |

66 | Designing networks for selfish users is hard
- Roughgarden
- 2001
(Show Context)
Citation Context ...der to influence the outcome of the game, when the interested party gives payments to agents on certain outcomes. A problem that relates to coordination mechanisms for selfish routing, and studied in =-=[21]-=-, asks to find a subnetwork of a given network that has optimal price of anarchy for a given total flow. This can be also cast as a special case of coordination mechanisms that allow either a given sp... |

65 | Bounding the inefficiency of equilibria in nonatomic congestion games - Roughgarden, Tardos - 2004 |

64 | Weak monotonicity suffices for truthfulness on convex domains
- Saks, Yu
- 2005
(Show Context)
Citation Context ...rithms with constant approximation ratio, in contrast to general domains where the current best upper bounds are linear with respect to n. 10 These domains are not convex and Theorem 1 of Saks and Yu =-=[30]-=- does not apply. Instead a more complicated property, the cycle monotonicity property [29], is necessary and sufficient for this domain (and every other domain): The cycle monotonicity property consid... |

62 | Approximate Equilibria and Ball Fusion
- Koutsoupias, Mavronicolas, et al.
- 2003
(Show Context)
Citation Context ...ulting allocation may be suboptimal. The price of anarchy, that is, the worst-case ratio of the maximum latency at a Nash equilibrium over the optimal allocation can be as high as Θ(log m/ log log m) =-=[11, 5, 10]-=-. The question is “How can we improve ⋆ Research supported in part by the IST (FLAGS, IST-2001-33116) program and by NSF.sthe price of anarchy?”; and what mechanisms one can use to improve the overall... |

57 | Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games
- Fleischer, Jain, et al.
- 2004
(Show Context)
Citation Context ...convince the players to reveal their true values (truthfulness) by paying them, while simultaneously optimize (as much possible) the system objective. In the latter class of problems (see for example =-=[13, 12, 16, 20, 21]-=-), the objective of the designer is to determine optimal taxes on the edges that result in an optimal routing, assuming that the players’ objective is affected by the taxes imposed. Our approach gener... |

56 | On the price of anarchy and stability of correlated equilibria of linear congestion games
- Christodoulou, Koutsoupias
- 2005
(Show Context)
Citation Context ...relation between the potential and the social cost of a set of strategies; based on these, we give a coordination mechanism with price of anarchy n for series-parallel network congestion games. 1 See =-=[4, 10, 9, 1]-=- for results on price of anarchy of congestion games for linear and polynomial latency functions. In this work, we consider general latencies.1.2 Related work Mechanisms to improve coordination of se... |

45 |
Algorithms for selfish agents
- Nisan
- 1999
(Show Context)
Citation Context ...e weight of the players that participate. Also, the algorithmic and communication issues involved in mechanism design seem to be completely different than the ones involved in coordination mechanisms =-=[31, 30, 34, 3]-=-. The idea of designing games to improve coordination appears also in the work of Korilis, Lazar, and Orda [24] but there the goal is to design games with a unique Nash equilibrium; there is no attemp... |

45 |
Éva Tardos. Truthful mechanisms for one-parameter agents
- Archer
- 2001
(Show Context)
Citation Context ...ase the speed of a machine i, keeping all other speeds the same, the new workload on machine i can only decrease. 14 The mechanism design version of the problem was first studied by Archer and Tardos =-=[3]-=-. It is a very important problem in Algorithmic Mechanism Design, because it’s a typical single-parameter problem, which means that each player has only one real private value and his objective is pro... |

44 | Edge pricing of multicommodity networks for heterogeneous selfish users with elastic demands
- Karakostas, Kolliopoulos, et al.
- 2006
(Show Context)
Citation Context ...convince the players to reveal their true values (truthfulness) by paying them, while simultaneously optimize (as much possible) the system objective. In the latter class of problems (see for example =-=[13, 12, 16, 20, 21]-=-), the objective of the designer is to determine optimal taxes on the edges that result in an optimal routing, assuming that the players’ objective is affected by the taxes imposed. Our approach gener... |

42 | Truthful mechanism design for multidimensional covering problems
- Minoeei, Swamy
- 2012
(Show Context)
Citation Context ...iven by x1j = t22j t21j + t 2 2j x2j = t21j t21j + t 2 2j . The mechanism has approximation ratio n+12 and this is optimal for taskindependent mechanisms. Restricted Domain mechanisms: Lavi and Swamy =-=[20]-=- studied two cases where the valuation domain is restricted. Instead of allowing tij to get any positive real values, they restrict the values to 2: low and high. They show that in such domains there ... |

39 |
A lower bound for scheduling mechanisms
- Christodoulou, Koutsoupias, et al.
- 2007
(Show Context)
Citation Context ...In other words, the lower bounds apply even to exponential-time algorithms. Nisan and Ronen [28] gave a lower bound of 2 for any truthful deterministic mechanism for 2 machines‡. Christodoulou et al. =-=[6]-=- improved the lower bound to 1+ √ 2 = 2.41 for 3 or more machines, and Koutsoupias and Vidali [17] to 1 + φ ≈ 2.61 for n machines where n is arbitrarily large. It is a major open problem to close the ... |

36 | Algorithms for Selfish Agents: Mechanism Design for Distributed Computation
- Nisan
- 1999
(Show Context)
Citation Context ...ism is a way to introduce traffic lights. Also, the algorithmic and communication issues involved in mechanism design seem to be completely different than the ones involved in coordination mechanisms =-=[16, 15, 19, 1]-=-. The idea of designing games to improve coordination appears also in the work of Korilis, Lazar, and Orda [9] but there the goal is to design games with a unique Nash equilibrium; there is no attempt... |

35 | Bounds for List Schedules on Uniform Processors - Cho, Sahni - 1980 |

34 |
Fast monotone 3-approximation algorithm for scheduling related machines
- Kovács
- 2005
(Show Context)
Citation Context ...os (Section 6.1) and has approximation ratio 5. To overcome the problem of derandomizing imposed by monotonicity they modify the speed set. The currently best deterministic algorithm is due to Kovacs =-=[18]-=-. The algorithm first rounds the speeds down to the closest power of 2, i.e. di = 2⌊log si⌋. Then it runs the well-known algorithm Longest Processing Time first (LPT) on the modified speed vector d. F... |

33 | Exact Price of Anarchy for Polynomial Congestion Games
- Aland, Dumrauf, et al.
(Show Context)
Citation Context |

33 | Coordination mechanisms for selfish scheduling
- Immorlica, Li, et al.
- 2005
(Show Context)
Citation Context ... allow either a given specific delay function or infinity (and fixed total flow). Following the conference version of this work [11] a few publications studied coordination mechanisms. In particular, =-=[19, 22]-=- study coordination mechanisms for the selfish task allocation, while [2, 8] consider truthful mechanisms for the same problem. Recently, Azar et al. [5] and Caragiannis [6] consider coordination mech... |

32 | Truthful approximation schemes for single-parameter agents
- Dhangwatnotai, Dobzinski, et al.
- 2008
(Show Context)
Citation Context ...o explore the interplay between truthfulness and computational complexity. It is a major open problem whether a deterministic monotone PTAS exists for this problem§. A very recent breakthrough result =-=[9]-=- shows that there exists a randomized truthful-in-expectation PTAS. In contrast to the scheduling problem of unrelated machines, in this special case there exist truthful mechanisms that output an opt... |

31 |
Mechanisms for Discrete Optimization with Rational Agents
- Archer
- 2004
(Show Context)
Citation Context ...ithm run in polynomial time. 15 6.1 Randomized mechanisms We will discuss 2 mechanisms in this section. The first mechanism is due to Archer and Tardos [3] and has approximation ratio 3. Later Archer =-=[2]-=- improved the randomized rounding procedure obtaining a 2-approximate mechanism. The second mechanism is due to Dhangwatnotai et al. [9] and is a randomized PTAS. Both mechanisms are truthful-in-expec... |

30 | Setting lower bounds on truthfulness
- Mu’alem, Schapira
- 2007
(Show Context)
Citation Context ...d it works as follows: For every task j, with probability 1/2 the algorithm gives the item to the minimizer of min{t1j , 43t2j}, and with 1/2 to the minimizer ofmin{t2j , 43t1j}. Mu’alem and Schapira =-=[24]-=- extended the mechanism for n machines which gives approximation ratio 1.875n. Recently, the result of Nisan and Ronen for 2 machines was improved by Lu and Yu [22] who gave a 1.67-approximation mecha... |

26 |
On the complexity of pure equilibria
- Fabrikant, Papadimitriou, et al.
- 2004
(Show Context)
Citation Context ...ile [2, 7] considered truthful mechanisms for the same problem. Recently, Azar et al. [5] considered coordination mechanisms for selfish scheduling on unrelated machines. 2 The Model Congestion games =-=[34, 27, 14]-=-, introduced by Rosenthal, is an important class of games that capture many aspects of selfish behavior in networks. A congestion game is defined by a tuple (N,M,(Σi)i∈N,(c j )j∈M) where N is the set ... |