Coalitional equilibria in non-cooperative games with strategic substitutes : Self-enforcing coalition deviations and irreversibility

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Abstract

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Introducing a coalitional equilibrium with restricted deviations, we examine how effectively equilibria based on coalitional stability refine Nash equilibria in games with σ-strategic substitutes and σ-monotone externalities. From the existing equilibria such as coalition-proof Nash equilibria and near-strong Nash equilibria, we can consider several ways to restrict coalitional deviations. We incorporate two natural self-enforcing conditions of coalition deviations, Nash stability and irreversibility, into the coalitional equilibrium and provide a more general analysis than earlier studies. We find it impossible that in each of the two stability concepts, the coalitional equilibrium effectively refines the Nash equilibrium for all games with σ-strategic substitutes and σ-monotone externalities.

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