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Combinatorial Optimization and Coalition Games

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Handbook of Combinatorial Optimization

Abstract

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 : 2N → 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 : N → R. 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 i∈S x i . A vector x is called an imputation if x(N) = υ(N), and ∀i∈ N : x i ≥ υ({i}) (individual rationality).

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Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, China

    Xiaotie Deng

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  1. Xiaotie Deng
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Editors and Affiliations

  1. University of Minnesota, Minneapolis, USA

    Ding-Zhu Du

  2. University of Florida, Gainesville, USA

    Panos M. Pardalos

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© 1998 Kluwer Academic Publishers

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Deng, X. (1998). Combinatorial Optimization and Coalition Games. In: Du, DZ., Pardalos, P.M. (eds) Handbook of Combinatorial Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0303-9_12

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  • DOI: https://doi.org/10.1007/978-1-4613-0303-9_12

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7987-4

  • Online ISBN: 978-1-4613-0303-9

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