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By Georgios Chalkiadakis, Edith Elkind, Visit Amazon's Michael Wooldridge Page, search results, Learn about Author Central, Michael Wooldridge,

Cooperative video game conception is a department of (micro- )economics that stories the habit of self-interested brokers in strategic settings the place binding agreements between brokers are attainable. Our objective during this publication is to offer a survey of labor at the computational elements of cooperative online game concept. we start through officially defining transferable software video games in attribute functionality shape, and introducing key solution Read more...

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Extra resources for Computational aspects of cooperative game theory

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An outcome of G is a pair (CS, x), where CS is a coalition structure over G and x is a payoff vector for CS. Given a payoff vector x, we write x(C) to denote the total payoff i∈C xi of a coalition C ⊆ N under x; we will use similar notation for other n-dimensional vectors throughout the book. 4, let us consider them one by one. The first requirement in the definition of a coalition structure states that every player must appear in some coalition; the second says that a player cannot appear in more than one coalition.

Conversely, an outcome is unstable if a coalition can benefit even by a tiny amount from deviating. This is a fairly strong requirement. In many situations, a deviation may be costly, and it would only make sense for a coalition to deviate if the gain from a deviation exceeded the costs of deviation. So, we might naturally consider relaxing the notion of the core, and only require that no coalition can benefit significantly by deviating. 28 An outcome x is said to be in the ε-core of a superadditive game G for some ε ∈ R if x(C) ≥ v(C) − ε for each C ⊆ N.

3 becomes a simple game if we rescale the payoffs so that v(N) = 1. In a simple game, coalitions of value 1 are said to be winning, and coalitions of value 0 are said to be losing. Such games can model situations where there is a task to be completed: a coalition is winning if and only if it can complete the task. Note that simple games are superadditive only if the complement of each winning coalition is losing. Clearly, there exist simple games that are not superadditive. Nevertheless, it is usually assumed that the outcome of a simple game is a payoff vector for the grand coalition, just as in superadditive games.

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