Combinatorial Optimization and Coalition Games

  • Xiaotie Deng


Studies on games in coalition form deal with the power of cooperation among its participants. In this sense it is often referred to as cooperative game theory. In a simple mathematical formulation, we have a set N of agents, and a value function υ : 2 N R where, for each subset S ⊆ N, , υ (S) represents the value obtained by the coalition of agents of the subset S without assistance of other agents, with υ(ø) = 0. Individual income can be represented by a vector x : NR. We consider games with side payments. The main issue here is how to fairly distribute the income collectively earned by a group of cooperating participants in the game. For simplicity, we write x(S) = Σ iS x i . A vector x is called an imputation if x(N) = υ(N), and ∀iN : x i υ({i}) (individual rationality).


Cooperative Game Solution Concept Coalition Game Balance Game Cooperative Game Theory 
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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Xiaotie Deng
    • 1
  1. 1.Department of Computer ScienceCity University of Hong KongKowloon, Hong KongChina

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