A Generalised $\lambda$-Core Concept for Normal Form Games

TL;DR

This paper introduces a generalized $$-Core concept for normal form games, demonstrating its non-emptiness in certain classes and highlighting limitations in broader contexts.

Contribution

It extends the $$-Core solution to a more general setting for non-cooperative games, identifying conditions for non-emptiness.

Findings

Non-empty for separable games with socially optimal Nash equilibrium

Examples show non-emptiness does not hold for all normal form games

Provides a framework for analyzing stability in generalized core concepts

Abstract

In this note we develop a generalisation of the $\lambda$-Core solution for non-cooperative games in normal form. We show that this generalised $\lambda$-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 $\lambda$-Core cannot be expected for large classes of normal form games.