## Efficiency Loss in a Network Resource Allocation Game: The Case of Elastic Supply (2004)

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Venue: | Mathematics of Operations Research |

Citations: | 141 - 10 self |

### BibTeX

@ARTICLE{Johari04efficiencyloss,

author = {Ramesh Johari and Shie Mannor and John N. Tsitsiklis},

title = {Efficiency Loss in a Network Resource Allocation Game: The Case of Elastic Supply},

journal = {Mathematics of Operations Research},

year = {2004},

volume = {29},

pages = {407--435}

}

### Years of Citing Articles

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### Abstract

We consider a resource allocation problem where individual users wish to send data across a network to maximize their utility, and a cost is incurred at each link that depends on the total rate sent through the link. It is known that as long as users do not anticipate the effect of their actions on prices, a simple proportional pricing mechanism can maximize the sum of users' utilities minus the cost (called aggregate surplus). Continuing previous efforts to quantify the effects of selfish behavior in network pricing mechanisms, we consider the possibility that users anticipate the effect of their actions on link prices. Under the assumption that the links' marginal cost functions are convex, we establish existence of a Nash equilibrium. We show that the aggregate surplus at a Nash equilibrium is no worse than a factor of 4 # 2 - 5 times the optimal aggregate surplus; thus, the efficiency loss when users are selfish is no more than approximately 34%.

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Citation Context ...to be a Nash equilibrium. Since the payoff of user r is concave, these necessary conditions will in fact be sufficient for w to be a Nash equilibrium. We begin with some concepts from convex analysis =-=[3, 23]-=-. An extended real-valued function is a function g : R → [−∞, ∞]; such a function is called proper if g(x) > −∞ for all x, and g(x) < ∞ for at least one x. We say that a scalar γ is a subgradient of a... |

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Citation Context ...re the network is treated as a market, and prices are set to mediate demand and supply of network resources; see, e.g., [5, 9]. We investigate a specific price mechanism considered by Kelly et al. in =-=[16]-=- (motivated by the proposal made in [14]). For simplicity let us first consider the special case of a single link; in this case the mechanism works as follows. Each user submits a bid, or total willin... |

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Citation Context ... if users do not anticipate the effect of their bid on the price, such 1a scheme maximizes the sum of users’ utilities minus the cost of the total allocated rate, known as the aggregate surplus (see =-=[20]-=-, Chapter 10). The pricing mechanism of [16] takes as input the bids of the users, and produces as output the price of the link, and the resulting rate allocation to the users. Kelly et al. [16] conti... |

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Citation Context ...nd prices are set to mediate demand and supply of network resources; see, e.g., [5, 9]. We investigate a specific price mechanism considered by Kelly et al. in [16] (motivated by the proposal made in =-=[14]-=-). For simplicity let us first consider the special case of a single link; in this case the mechanism works as follows. Each user submits a bid, or total willingness-to-pay, to the link manager. This ... |

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Citation Context ... investigation forms part of a broader body of work on quantifying efficiency loss in environments where participants are selfish. Results have been obtained for routing [7, 17, 21], traffic networks =-=[6, 25]-=- and network design problems [1, 8]. Our work is most closely related to that of [12], where the same market mechanism as in this paper was considered for the case where the supply of a link is fixed,... |

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Citation Context ...er f ≥ 0 with p(0) = 0, such that for f ≥ 0: C(f) = ∫ f Thus C(f) is strictly convex and strictly increasing. 0 p(z)dz. Concavity in Assumption 1 corresponds to elastic traffic, as defined by Shenker =-=[26]-=-; such traffic includes file transfers such as FTP connections and peer-to-peer connections. Note that Assumption 2 does not require the price function p to be differentiable. Indeed, assuming smoothn... |

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Citation Context ...lves with the specific interpretation of the cost function at the link. (An insightful discussion of the relationship between active queue management and the cost function of the link may be found in =-=[10]-=-.) In this paper, we investigate the robustness of the market mechanism of [16] when users attempt to manipulate the market. Formally, we consider a model where users anticipate the effects of their a... |

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Citation Context ...ion. Indeed, much of the interest in this market mechanism stems from its desirable properties as a decentralized system, including both stability and scalability. For details, we refer the reader to =-=[11, 13, 27, 28]-=-. One important interpretation of the price given to users in the algorithms of [16] is that it can provide early notification of congestion. Building on the Explicit Congestion Notification (ECN) pro... |

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Citation Context ...e in wr (since Ur is concave and strictly increasing, and dr(w) is concave in wr); and the strategy space of each user r is a compact, convex, nonempty subset of R. Applying Rosen’s existence theorem =-=[24]-=-, we conclude that a Nash equilibrium w exists for this game. ✷ In the remainder of this section, we establish necessary and sufficient conditions for a vector w to be a Nash equilibrium. Because the ... |

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Citation Context ...stion before the link’s true capacity is actually met). Many proposals have been made for “active queue management” (AQM) to achieve good performance with Explicit Congestion Notification; see, e.g., =-=[2, 15, 18, 19]-=-. This issue is of secondary importance to our discussion, as we do not concern ourselves with the specific interpretation of the cost function at the link. (An insightful discussion of the relationsh... |

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Citation Context ...stion before the link’s true capacity is actually met). Many proposals have been made for “active queue management” (AQM) to achieve good performance with Explicit Congestion Notification; see, e.g., =-=[2, 15, 18, 19]-=-. This issue is of secondary importance to our discussion, as we do not concern ourselves with the specific interpretation of the cost function at the link. (An insightful discussion of the relationsh... |

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Citation Context ...er body of work on quantifying efficiency loss in environments where participants are selfish. Results have been obtained for routing [7, 17, 21], traffic networks [6, 25] and network design problems =-=[1, 8]-=-. Our work is most closely related to that of [12], where the same market mechanism as in this paper was considered for the case where the supply of a link is fixed, or inelastic; this was the mechani... |

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Citation Context ...stion before the link’s true capacity is actually met). Many proposals have been made for “active queue management” (AQM) to achieve good performance with Explicit Congestion Notification; see, e.g., =-=[2, 15, 18, 19]-=-. This issue is of secondary importance to our discussion, as we do not concern ourselves with the specific interpretation of the cost function at the link. (An insightful discussion of the relationsh... |

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Citation Context ...important interpretation of the price given to users in the algorithms of [16] is that it can provide early notification of congestion. Building on the Explicit Congestion Notification (ECN) proposal =-=[22]-=-, this interpretation suggests that the network might charge users proactively, in hopes of avoiding congestion at links later. From an implementation standpoint, such a shift implies that rather than... |

158 | Tight bounds for worst-case equilibria
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Citation Context ...re price anticipating. Such an investigation forms part of a broader body of work on quantifying efficiency loss in environments where participants are selfish. Results have been obtained for routing =-=[7, 17, 21]-=-, traffic networks [6, 25] and network design problems [1, 8]. Our work is most closely related to that of [12], where the same market mechanism as in this paper was considered for the case where the ... |

153 |
Convex Analysis and Optimization. Athena Scientic
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Citation Context ...to be a Nash equilibrium. Since the payoff of user r is concave, these necessary conditions will in fact be sufficient for w to be a Nash equilibrium. We begin with some concepts from convex analysis =-=[3, 23]-=-. An extended real-valued function is a function g : R → [−∞, ∞]; such a function is called proper if g(x) > −∞ for all x, and g(x) < ∞ for at least one x. We say that a scalar γ is a subgradient of a... |

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Citation Context ...ion. Indeed, much of the interest in this market mechanism stems from its desirable properties as a decentralized system, including both stability and scalability. For details, we refer the reader to =-=[11, 13, 27, 28]-=-. One important interpretation of the price given to users in the algorithms of [16] is that it can provide early notification of congestion. Building on the Explicit Congestion Notification (ECN) pro... |

119 | Near-optimal network design with selfish agents
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Citation Context ...er body of work on quantifying efficiency loss in environments where participants are selfish. Results have been obtained for routing [7, 17, 21], traffic networks [6, 25] and network design problems =-=[1, 8]-=-. Our work is most closely related to that of [12], where the same market mechanism as in this paper was considered for the case where the supply of a link is fixed, or inelastic; this was the mechani... |

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

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Citation Context |

83 | On the stability of networks operating TCPlike congestion control
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Citation Context ...ion. Indeed, much of the interest in this market mechanism stems from its desirable properties as a decentralized system, including both stability and scalability. For details, we refer the reader to =-=[11, 13, 27, 28]-=-. One important interpretation of the price given to users in the algorithms of [16] is that it can provide early notification of congestion. Building on the Explicit Congestion Notification (ECN) pro... |

74 | Selfish routing in capacitated networks
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Citation Context ... investigation forms part of a broader body of work on quantifying efficiency loss in environments where participants are selfish. Results have been obtained for routing [7, 17, 21], traffic networks =-=[6, 25]-=- and network design problems [1, 8]. Our work is most closely related to that of [12], where the same market mechanism as in this paper was considered for the case where the supply of a link is fixed,... |

40 |
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Citation Context ...work performance. This has led to a surge of interest in congestion pricing, where the network is treated as a market, and prices are set to mediate demand and supply of network resources; see, e.g., =-=[5, 9]-=-. We investigate a specific price mechanism considered by Kelly et al. in [16] (motivated by the proposal made in [14]). For simplicity let us first consider the special case of a single link; in this... |

16 | A market managed multi-service internet
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Citation Context ...work performance. This has led to a surge of interest in congestion pricing, where the network is treated as a market, and prices are set to mediate demand and supply of network resources; see, e.g., =-=[5, 9]-=-. We investigate a specific price mechanism considered by Kelly et al. in [16] (motivated by the proposal made in [14]). For simplicity let us first consider the special case of a single link; in this... |

1 | Stability and fairness of end-to-end congestion control - Kelly |