“Beat-Your-Rival” Routing Games

Blocq, Gideon; Orda, Ariel

doi:10.1007/978-3-662-48433-3_18

Cited by 1 publication

(3 citation statements)

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“…In other words, at a balanced flow profile, every possible path with positive flow has the same cost for its worst-case link. In [39], the next lemma is proven.…”

Section: The Routing Game Nucleolusmentioning

confidence: 85%

“…Hence, from (38) and (39), J S ( f N \S , f S ) ≥ J S ( f N \S , f S ) > J S ( f N \S , f S ). Now that we have constructed a systemoptimal flow profile f , we can decide on how to split its cost among the individual users.…”

Section: The Corementioning

confidence: 92%

“…We now continue to describe the RGN. Before doing so, we bring the following definition from [39]. Definition 3.4.…”

Section: The Routing Game Nucleolusmentioning

confidence: 99%

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Coalitions in Routing Games: A Worst-Case Perspective

Blocq

Orda

2019

IEEE Trans. Netw. Sci. Eng.

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We investigate a routing game that allows for the creation of coalitions, within the framework of cooperative game theory. Specifically, we describe the cost of each coalition as its maximin value. This represents the performance that the coalition can guarantee itself, under any (including worst) conditions. We then investigate fundamental solution concepts of the considered cooperative game, namely the core and a variant of the min-max fair nucleolus. We consider two types of routing games based on the agents' Performance Objectives, namely bottleneck routing games and additive routing games. For bottleneck games we establish that the core includes all system-optimal flow profiles and that the nucleolus is system-optimal or disadvantageous for the smallest agent in the system. Moreover, we describe an interesting set of scenarios for which the nucleolus is always system-optimal. For additive games, we focus on the fundamental load balancing game of routing over parallel links. We establish that, in contrary to bottleneck games, not all system-optimal flow profiles lie in the core. However, we describe a specific system-optimal flow profile that does lie in the core and, under assumptions of symmetry, is equal to the nucleolus.

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“…In other words, at a balanced flow profile, every possible path with positive flow has the same cost for its worst-case link. In [39], the next lemma is proven.…”

Section: The Routing Game Nucleolusmentioning

confidence: 85%

Section: The Corementioning

confidence: 92%