Combinatorial Optimization and Coalition Games

• Xiaotie Deng
Chapter

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 : 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).

Keywords

Cooperative Game Solution Concept Coalition Game Balance Game Cooperative Game Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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