Weighted congestion games with separable preferences

Milchtaich, Igal

doi:10.1016/j.geb.2009.03.009

Cited by 27 publications

(11 citation statements)

References 16 publications

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“…Both networks are considerably simpler than the one constructed in the proof of Theorem 2. For an example of a simple representation of a specific variety of congestion games as weighted network congestion games, see [2].…”

Section: Presentation Resultsmentioning

confidence: 99%

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Representation of finite games as network congestion games

Milchtaich

2012

Int J Game Theory

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Abstract-Weighted network congestion games are used for modeling interactions involving finitely many non-identical users of network resources, such as road segments or communication links. In spite of their special form, these games are not fundamentally special: every finite game can be represented as a weighted network congestion game. The same is true for the class of unweighted network congestion games with player-specific costs, in which the players differ in their cost functions rather than their weights. The intersection of the two classes consists of the unweighted network congestion games. These games are special: a finite game can be represented in this form if and only if it is an exact potential game.

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Section: Presentation Resultsmentioning

confidence: 99%

“…Second, a weight is specified for each player , which represents the player's congestion impact. 2 The total weight of the players whose chosen route includes an edge is the flow (or load) on . The (not necessarily negative) cost of for each of its users is .…”

Section: Network Congestion Gamesmentioning

confidence: 99%

Representation of finite games as network congestion games

Milchtaich

2012

Int J Game Theory

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“…Note the game is weighted and it does not admit any potential function, and therefore, the results discussed at the end of Section 3.2 cannot be applied, the results discussed in [44] show that when the cost functions are separable, i.e., when the cost is defined as the product of a player-specific parameter and the congestion level, the game always admits a pure NE.…”

Section: Cost Function 2: Weighted Interference-ratementioning

confidence: 99%

Network Selection and Resource Allocation Games for Wireless Access Networks

Malanchini

Cesana

Gatti

2013

IEEE Trans. on Mobile Comput.

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Abstract-Wireless access networks are often characterized by the interaction of different end users, communication technologies, and network operators. This paper analyzes the dynamics among these "actors" by focusing on the processes of wireless network selection, where end users may choose among multiple available access networks to get connectivity, and resource allocation, where network operators may set their radio resources to provide connectivity. The interaction among end users is modeled as a noncooperative congestion game, where players (end users) selfishly select the access network that minimizes their perceived selection cost. A method based on mathematical programming is proposed to find Nash equilibria and characterize their optimality under three cost functions, which are representative of different technological scenarios. System level simulations are then used to evaluate the actual throughput and fairness of the equilibrium points. The interaction among end users and network operators is then assessed through a two-stage multileader/multifollower game, where network operators (leaders) play in the first stage by properly setting the radio resources to maximize their users, and end users (followers) play in the second stage the aforementioned network selection game. The existence of exact and approximated subgame perfect Nash equilibria of the two-stage game is thoroughly assessed and numerical results are provided on the "quality" of such equilibria.

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“…The congestion game is therefore weighted in the sense that not all users contribute to congestion in an identical manner. Fewer results exist for those games [4,23], even when user strategies only consist in choosing one resource among a strategy set that is identical for all players.…”

Section: Related Workmentioning

confidence: 99%

“…As a result, following [22,23] the game would be called a weighted congestion game with separable preferences, and can be transformed into an equivalent weighted congestion game with player-specific constants [21] (i.e., the payoffs of users selecting the same strategy only differ through a user-specific additive constant). In general, the existence of an equilibrium is not ensured for such games when the number of users is finite [21,22,23]. In the nonatomic case, the existence of a mixed equilibrium is ensured by [31] and the loss of efficiency due to user selfishness is bounded [4], but the existence of a pure equilibrium in the general case is not guaranteed.…”

Section: Related Workmentioning

confidence: 99%