Combinatorial Optimization and Coalition Games

Xiaotie Deng ()
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Xiaotie Deng: City University of Hong Kong, Department of Computer Science

A chapter in Handbook of Combinatorial Optimization, 1998, pp 823-849 from Springer

Abstract: 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 : 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 : 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).

Keywords: Cooperative Game; Solution Concept; Coalition Game; Balance Game; Cooperative Game Theory (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-0303-9_12

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DOI: 10.1007/978-1-4613-0303-9_12

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