Efficient stabilization of cooperative matching games

Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Cooperative matching games have drawn much interest partly because of the connection with bargaining solutions in the networking environment. However, it is not always guaranteed that a network under investigation gives rise to a stable bargaining outcome. To address this issue, we consider a modification process, called stabilization, that yields a network with stable outcomes, where the modification should be as small as possible. Therefore, the problem is cast to a combinatorial-optimization problem in a graph. Recently, the stabilization by edge removal was shown to be NP-hard. On the contrary, in this paper, we show that other possible ways of stabilization, namely, edge addition, vertex removal and vertex addition, are all polynomial-time solvable. Thus, we obtain a complete complexity-theoretic classification of the natural four variants of the network stabilization problem. We further study weighted variants and prove that the variants for edge addition and vertex removal are NP-hard.

Original languageEnglish
Pages (from-to)69-82
Number of pages14
JournalTheoretical Computer Science
Volume677
DOIs
Publication statusPublished - 2017 May 16
Externally publishedYes

Keywords

  • Cooperative game
  • Core
  • Gallai–Edmonds decomposition
  • Matching
  • Network bargaining
  • Solution concept

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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