Mathematical Programming

, Volume 87, Issue 3, pp 441–452 | Cite as

Totally balanced combinatorial optimization games

  • Xiaotie Deng
  • Toshihide Ibaraki
  • Hiroshi Nagamochi
  • Wenan Zang

Abstract.

Combinatorial optimization games deal with cooperative games for which the value of every subset of players is obtained by solving a combinatorial optimization problem on the resources collectively owned by this subset. A solution of the game is in the core if no subset of players is able to gain advantage by breaking away from this collective decision of all players. The game is totally balanced if and only if the core is non-empty for every induced subgame of it.¶We study the total balancedness of several combinatorial optimization games in this paper. For a class of the partition game [5], we have a complete characterization for the total balancedness. For the packing and covering games [3], we completely clarify the relationship between the related primal/dual linear programs for the corresponding games to be totally balanced. Our work opens up the question of fully characterizing the combinatorial structures of totally balanced packing and covering games, for which we present some interesting examples: the totally balanced matching, vertex cover, and minimum coloring games.

Key words: combinatorial optimization – duality theory – cooperative games – total balancedness 
Mathematics Subject Classification (1991): 90D12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Xiaotie Deng
    • 1
  • Toshihide Ibaraki
    • 2
  • Hiroshi Nagamochi
    • 2
  • Wenan Zang
    • 3
  1. 1.Department of Computer Science, City University of Hong Kong, Hong Kong, P.R. China, e-mail: deng@cs.cityu.edu.hkCN
  2. 2.Department of Applied Mathematics and Physics, Graduate School of Information, Kyoto University, Kyoto, Japan 606-8501, e-mail: {ibaraki,naga}@kyoto-u.ac.jpJP
  3. 3.Department of Mathematics, The University of Hong Kong, Hong Kong, P.R. China, e-mail: wzang@maths.hku.hkCN

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