Population Monotonicity in Matching Games

Han, Xiao; Fang, Qizhi

doi:10.48550/arxiv.2105.00621

Cited by 1 publication

(1 citation statement)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They showed that the core of assignment games is always non-empty, and characterized the core allocations by using matching theory, LP duality theory, and their highly nontrivial interplay. Since then, matching games have attracted a lot of research efforts, and various allocation concepts have been studied within different settings [17,7,6,9,10,21]. In particular, Vazirani [20] studied the approximate core for matching games and achieved the best possible approximate ratio.…”

Section: Our Contributionsmentioning

confidence: 99%

Approximate Core Allocations for Multiple Partners Matching Games

Han¹,

Lu²,

Fang³

2021

Preprint

Self Cite

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