## Near-optimal network design with selfish agents (2003)

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Venue: | IN PROCEEDINGS OF THE 35TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC |

Citations: | 119 - 20 self |

### BibTeX

@INPROCEEDINGS{Anshelevich03near-optimalnetwork,

author = {Elliot Anshelevich and Anirban Dasgupta and Éva Tardos and Tom Wexler},

title = {Near-optimal network design with selfish agents},

booktitle = {IN PROCEEDINGS OF THE 35TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC},

year = {2003},

pages = {511--520},

publisher = {}

}

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### Abstract

We introduce a simple network design game that models how independent selfish agents can build or maintain a large network. In our game every agent has a specific connectivity requirement, i.e. each agent has a set of terminals and wants to build a network in which his terminals are connected. Possible edges in the network have costs and each agent’s goal is to pay as little as possible. Determining whether or not a Nash equilibrium exists in this game is NP-complete. However, when the goal of each player is to connect a terminal to a common source, we prove that there is a Nash equilibrium as cheap as the optimal network, and give a polynomial time algorithm to find a (1 + ε)-approximate Nash equilibrium that does not cost much more. For the general connection game we prove that there is a 3-approximate Nash equilibrium that is as cheap as the optimal network, and give an algorithm to find a (4.65 + ε)-approximate Nash equilibrium that does not cost much more.

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Citation Context ...rice of anarchy to refer to this increase in cost caused by selfish behavior. The price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing =-=[5, 6, 13, 18]-=-, routing [17, 19, 20], facility location [22], and flow control [2, 7, 21]. In some cases [17, 19] the Nash equilibrium is unique, while in others [13] the best Nash equilibrium coincides with the op... |

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Citation Context ... to this increase in cost caused by selfish behavior. The price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing [5, 6, 13, 18], routing =-=[17, 19, 20]-=-, facility location [22], and flow control [2, 7, 21]. In some cases [17, 19] the Nash equilibrium is unique, while in others [13] the best Nash equilibrium coincides with the optimum solution and the... |

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Citation Context ...levant such model to our research is presented in [6] (and further addressed in [11,12,21]). In [6], extra restrictions of “fair sharing” are added to the Connection Game, making it a congestion game =-=[33]-=- and thereby guaranteeing some nice properties, like the existence of Nash equilibria and a bounded price of stability. While the connection game is not a congestion game, and is not guaranteed to hav... |

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Citation Context ...ntralized optimum of the connection game, i.e. the network of bought edges which minimizes the sum of the players’ contributions, is the classic network design problem of the generalized Steiner tree =-=[1, 10]-=-. 1sOur Results We are most interested in deterministic Nash equilibria of the connection game, and in the optimistic price of anarchy, as the pessimistic price of anarchy in our game can be quite bad... |

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Citation Context ...ntralized optimum of the connection game, i.e. the network of bought edges which minimizes the sum of the players’ contributions, is the classic network design problem of the generalized Steiner tree =-=[1, 10]-=-. 1sOur Results We are most interested in deterministic Nash equilibria of the connection game, and in the optimistic price of anarchy, as the pessimistic price of anarchy in our game can be quite bad... |

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Citation Context ...TOM WEXLER Schultz and Stier [37] study the ratio of the best equilibrium to the optimum, in the context of a capacitated routing game. We call this ratio the price of stability, a term introduced in =-=[6]-=-. 1 In this paper we consider a simple network design game where every agent has a specific connectivity requirement, i.e. each agent has a set of terminals and wants to build a network in which his t... |

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Citation Context ...lace this connection set with the cheapest deviation tree and run this algorithm over again. If we use a 2-approximate Steiner forest T , and an optimal Steiner tree 1.55-approximation algorithm from =-=[16]-=- as our subroutine, then the above algorithm actually gives a (4.65 + ε)-approximate Nash equilibrium on T ′ with c(T ′ ) ≤ 2 · OP T , in time polynomial in n and ε −1 . 10sAcknowledgements This proje... |

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181 | On a network creation game
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Citation Context ...el of how different service providers build and maintain the Internet topology. We use a game theoretic version of network design problems considered in approximation algorithms [22]. Fabrikant et al =-=[18]-=- study a different network creation game. Network games similar to that of [18] have also been studied for modeling the creation and maintenance of social networks [9,23]. In the network game consider... |

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Citation Context ... to this increase in cost caused by selfish behavior. The price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing [5, 6, 13, 18], routing =-=[17, 19, 20]-=-, facility location [22], and flow control [2, 7, 21]. In some cases [17, 19] the Nash equilibrium is unique, while in others [13] the best Nash equilibrium coincides with the optimum solution and the... |

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Citation Context ...rice of anarchy to refer to this increase in cost caused by selfish behavior. The price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing =-=[5, 6, 13, 18]-=-, routing [17, 19, 20], facility location [22], and flow control [2, 7, 21]. In some cases [17, 19] the Nash equilibrium is unique, while in others [13] the best Nash equilibrium coincides with the op... |

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Citation Context ...d players seek to establish a directed path from their terminal to the common source. Note that problems in directed graphs are often significantly more complicated than their undirected counterparts =-=[4, 9]-=-. Second, players do not have to insist on connecting their terminals at all cost, but rather each player i may have a maximum cost max(i) that he is willing to pay, and would rather stay unconnected ... |

119 | The price of selfish routing - Mavronicolas, Spirakis - 2001 |

117 | The price of anarchy in finite congestion games - Christodoulou, Koutsoupias - 2005 |

115 | Applications of approximation algorithms to cooperative games
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Citation Context ...sts in this manner. To keep our model simple, we assume that each agent’s goal is to keep his terminals connected, and agents are not sensitive to the length of the connecting path. Jain and Vazirani =-=[12]-=- study a different cost-sharing game related to Steiner trees. They assume that each player i has a utility ui for belonging to the Steiner tree. Their goal is to give a truthful mechanism to build a ... |

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Citation Context ...rice of anarchy to refer to this increase in cost caused by selfish behavior. The price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing =-=[5, 6, 13, 18]-=-, routing [17, 19, 20], facility location [22], and flow control [2, 7, 21]. In some cases [17, 19] the Nash equilibrium is unique, while in others [13] the best Nash equilibrium coincides with the op... |

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Citation Context ... by selfish behavior. The price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing [5, 6, 13, 18], routing [17, 19, 20], facility location =-=[22]-=-, and flow control [2, 7, 21]. In some cases [17, 19] the Nash equilibrium is unique, while in others [13] the best Nash equilibrium coincides with the optimum solution and the authors study the quali... |

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Citation Context ...he price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing [5, 6, 13, 18], routing [17, 19, 20], facility location [22], and flow control =-=[2, 7, 21]-=-. In some cases [17, 19] the Nash equilibrium is unique, while in others [13] the best Nash equilibrium coincides with the optimum solution and the authors study the quality of the worst equilibrium. ... |

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Citation Context |

65 | On Nash equilibria for a network creation game
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Citation Context ... a different network creation game. Network games similar to that of [18] have also been studied for modeling the creation and maintenance of social networks [9,23]. In the network game considered in =-=[3,9,18,23]-=- each agent corresponds to a single node of the network, and agents can only buy edges adjacent to their nodes. This model of network creation seems extremely well suited for modeling the creation of ... |

44 | Network design with weighted players
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Citation Context ...s paper [7], there have been several new papers about the connection game, e.g., [5,8,13,17,24–26]. Probably the most relevant such model to our research is presented in [6] (and further addressed in =-=[11,12,21]-=-). In [6], extra restrictions of “fair sharing” are added to the Connection Game, making it a congestion game [33] and thereby guaranteeing some nice properties, like the existence of Nash equilibria ... |

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Citation Context ...s paper [7], there have been several new papers about the connection game, e.g., [5,8,13,17,24–26]. Probably the most relevant such model to our research is presented in [6] (and further addressed in =-=[11,12,21]-=-). In [6], extra restrictions of “fair sharing” are added to the Connection Game, making it a congestion game [33] and thereby guaranteeing some nice properties, like the existence of Nash equilibria ... |

32 | Strong Equilibrium in cost sharing connection games - Epstein, Feldman, et al. - 2009 |

29 | On the price of stability for designing undirected networks with fair cost allocations
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Citation Context ...s paper [7], there have been several new papers about the connection game, e.g., [5,8,13,17,24–26]. Probably the most relevant such model to our research is presented in [6] (and further addressed in =-=[11,12,21]-=-). In [6], extra restrictions of “fair sharing” are added to the Connection Game, making it a congestion game [33] and thereby guaranteeing some nice properties, like the existence of Nash equilibria ... |

27 |
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Citation Context ... to this increase in cost caused by selfish behavior. The price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing [5, 6, 13, 18], routing =-=[17, 19, 20]-=-, facility location [22], and flow control [2, 7, 21]. In some cases [17, 19] the Nash equilibrium is unique, while in others [13] the best Nash equilibrium coincides with the optimum solution and the... |

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Citation Context ...nals connected, and agents are not sensitive to the length of the connecting path. Since the conference version of this paper [5], there have been several new papers about the connection game, e. g., =-=[14, 22, 21, 23, 11, 6]-=-. Probably the most relevant such model to our research is presented in [4] (and further addressed in [9, 10, 18]). In [4], extra restrictions of “fair sharing” are added to the Connection Game, makin... |

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Citation Context ...nals connected, and agents are not sensitive to the length of the connecting path. Since the conference version of this paper [5], there have been several new papers about the connection game, e. g., =-=[14, 22, 21, 23, 11, 6]-=-. Probably the most relevant such model to our research is presented in [4] (and further addressed in [9, 10, 18]). In [4], extra restrictions of “fair sharing” are added to the Connection Game, makin... |

11 | Non-cooperative facility location and covering games
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Citation Context ...nals connected, and agents are not sensitive to the length of the connecting path. Since the conference version of this paper [5], there have been several new papers about the connection game, e. g., =-=[14, 22, 21, 23, 11, 6]-=-. Probably the most relevant such model to our research is presented in [4] (and further addressed in [9, 10, 18]). In [4], extra restrictions of “fair sharing” are added to the Connection Game, makin... |

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Eyal Even-Dar, Yishay Mansour, and Liam Roditty. On Nash equilibria for a network creation game
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Citation Context ...a different network creation game. Network games similar to that of [15] have also been studied for modeling the creation and maintenance of social networks [7, 20]. In the network game considered in =-=[7, 15, 20, 3]-=- each agent corresponds to a single node of the network, and agents can only buy edges adjacent to their nodes. This model of network creation seems extremely well suited for modeling the creation of ... |

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Citation Context ...he price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing [5, 6, 13, 18], routing [17, 19, 20], facility location [22], and flow control =-=[2, 7, 21]-=-. In some cases [17, 19] the Nash equilibrium is unique, while in others [13] the best Nash equilibrium coincides with the optimum solution and the authors study the quality of the worst equilibrium. ... |

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Citation Context ... algorithms [10]. Fabrikant et al [8] study a different network creation game. Network games similar to that of [8] have also been studied for modeling the creation and maintenance of social networks =-=[3, 11]-=-. In the network game considered in [3, 8, 11] each agent corresponds to a single node of the network, and agents can only buy edges adjacent to their nodes. This model of 2snetwork creation seems ext... |

7 |
Roughgarden and Éva Tardos. How bad is selfish routing
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Citation Context ...o this increase in cost caused by selfish behavior. The price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing [11, 12, 25, 29], routing =-=[30, 31, 32]-=-, facility location [34], and flow control [2, 13, 33]. In some cases [30, 31] the Nash equilibrium is unique, while in others [25] the best Nash equilibrium coincides with the optimum solution and th... |

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Citation Context ...d players seek to establish a directed path from their terminal to the common source. Note that problems in directed graphs are often significantly more complicated than their undirected counterparts =-=[8, 16]-=-. Second, players do not have to insist on connecting their terminals at all cost, but rather each player i may have a maximum cost max(i) that he is willing to pay, and would rather stay unconnected ... |

5 | Price of Stability in Survivable Network Design - Anshelevich, Caskurlu - 2009 |

5 | The Price of Sel Routing - Mavronicolas, Spirakis - 2001 |

5 |
AND VIJAY VAZIRANI: Applications of approximation algorithms to cooperative games
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Citation Context ...out some overseeing authority. However, as we show in this paper, is still possible to nudge the agents into an extremely good outcome without restricting their behavior in any way. Jain and Vazirani =-=[24]-=- study a different cost-sharing game related to Steiner trees. They assume that each player i has a utility ui for belonging to the Steiner tree, and that ui is a private value. Their goal is to give ... |

5 |
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Citation Context ...evant such model to our research is presented in [4] (and further addressed in [9, 10, 18]). In [4], extra restrictions of “fair sharing” are added to the Connection Game, making it a congestion game =-=[28]-=- and thereby guaranteeing some nice properties, like the existence of Nash equilibria even with multiple terminals per player, and a bounded price of stability. While the connection game is not a cong... |

4 |
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Citation Context ...d players seek to establish a directed path from their terminal to the common source. Note that problems in directed graphs are often significantly more complicated than their undirected counterparts =-=[4, 9]-=-. Second, players do not have to insist on connecting their terminals at all cost, but rather each player i may have a maximum cost max(i) that he is willing to pay, and would rather stay unconnected ... |

4 | Selfish tra#c allocation for server farms - Czumaj, Krysta, et al. - 2002 |

4 | Performance of user equilibria in tra#c networks - Schulz, Moses - 2003 |

3 |
Éva Tardos, Tom Wexler, Near-optimal network design with selfish agents
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(Show Context)
Citation Context ...ep our model simple, we assume that each agent’s goal is to keep his terminals connected, and agents are not sensitive to the length of the connecting path. Since the conference version of this paper =-=[5]-=-, there have been several new papers about the connection game, e. g., [14, 22, 21, 23, 11, 6]. Probably the most relevant such model to our research is presented in [4] (and further addressed in [9, ... |

3 |
SVETLANA OLONETSKY, AND RONEN SHABO: On the price of stability for designing undirected networks with fair cost allocations
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(Show Context)
Citation Context ... [5], there have been several new papers about the connection game, e. g., [14, 22, 21, 23, 11, 6]. Probably the most relevant such model to our research is presented in [4] (and further addressed in =-=[9, 10, 18]-=-). In [4], extra restrictions of “fair sharing” are added to the Connection Game, making it a congestion game [28] and thereby guaranteeing some nice properties, like the existence of Nash equilibria ... |

2 |
On a Network Creation Game. Unpublished manuscript
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(Show Context)
Citation Context ...el of how different service providers build and maintain the Internet topology. We use a game theoretic version of network design problems considered in approximation algorithms [10]. Fabrikant et al =-=[8]-=- study a different network creation game. Network games similar to that of [8] have also been studied for modeling the creation and maintenance of social networks [3, 11]. In the network game consider... |

2 |
Koutsoupias, The price of anarchy of finite congestion games
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(Show Context)
Citation Context ...rice of anarchy to refer to this increase in cost caused by selfish behavior. The price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing =-=[11, 12, 25, 29]-=-, routing [30, 31, 32], facility location [34], and flow control [2, 13, 33]. In some cases [30, 31] the Nash equilibrium is unique, while in others [25] the best Nash equilibrium coincides with the o... |

2 |
CZUMAJ AND BERTHOLD VÖCKING: Tight bounds for worst-case equilibria
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Citation Context ...rice of anarchy to refer to this increase in cost caused by selfish behavior. The price of anarchy has been studied in a number of games dealing with various networking issues, such as load balancing =-=[11, 12, 25, 29]-=-, routing [30, 31, 32], facility location [34], and flow control [2, 13, 33]. In some cases [30, 31] the Nash equilibrium is unique, while in others [25] the best Nash equilibrium coincides with the o... |

1 | The price of routing unsplittable flow. newblock - Awerbuch, Azar, et al. - 2005 |