On the Complexity of Nucleolus Computation for Bipartite b-Matching Games

Koenemann, Jochen; Toth, Justin; Zhou, Felix

doi:10.48550/arxiv.2105.07161

Cited by 1 publication

(3 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consider a network of companies such that any connected pair of companies can enter a deal with revenue, and at any time every company has the capacity to fulfill a limited number of deals. The scenario above, taken from [11], can be modeled as the multiple partners matching game [18,5], which generalizes the matching game [6,4,9,10] to allow each player to have more than one partner. Such a multiple partners setting makes the game more applicable to the real world and more attractive to researchers [16,8,19,4,5].…”

Section: Background and Motivationmentioning

confidence: 99%

“…The multiple partners matching game, which is also known as the b-matching game [6,12,11], is defined as follows. Through the paper, let G = (V, E) denote an undirected graph with an integral vertex capacity function b and an edge weight function w. For any vertex v, δ(v) dentoes the set of edges incident to v. An integral vector x ∈ Z E is a b-matching of G if it satisfies constraints (1) and ( 2) A central question in cooperative game theory is to allocate the total profit generated through cooperation among individual players.…”

Section: Background and Motivationmentioning

confidence: 99%

“…Könemann, Toth and Zhou [11] discussed the complexity of nucleolus computation in multiple partners assignment games.…”

Section: Our Contributionsmentioning

confidence: 99%

See 2 more Smart Citations

Approximate Core Allocations for Multiple Partners Matching Games

Han¹,

Lu²,

Fang³

2021

Preprint

View full text Add to dashboard Cite

The multiple partners matching game is a cooperative profit-sharing game, which generalizes the classic matching game by allowing each player to have more than one partner. The core is one of the most important concepts in cooperative game theory, which consists all possible ways of allocating the worth of the game among individual players such that the grand coalition remains intact. For the multiple partners matching game, the core may be empty in general [6]; even when the core is non-empty, the core membership problem is intractable in general [5]. Thus we study approximate core allocations for the multiple partners matching game, and provide an LP-based mechanism guaranteeing that no coalition is paid less than 2 3 times the profit it makes on its own. Moreover, we show that the factor 2 3 is best possible in general, but can be improved depending on how severely constrained the players are. Our result generalizes the recent work of Vazirani [20] from matching games to multiple partners matching games.

show abstract