In this note we develop a generalisation of the λ-Core solution for non-cooperative games in normal form. We show that this generalised λ-Core is non-empty for the class of separable games that admit a socially optimal Nash equilibrium. Examples are provided that indicate that non-emptiness of the generalised λ-Core cannot be expected for large classes of normal form games.
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Chakrabarti et al. (2024) studied this question.
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