On the nonemptiness of approximate cores of large games

We provide a new proof of the nonemptiness of approximate cores of games with many players of a finite number of types. Earlier papers in the literature proceed by showing that, for games with many players, equal-treatment cores of their “balanced cover games,” which are nonempty, can be approximated by equal-treatment \varepsilon ? -cores of the games themselves. Our proof is novel in that we develop a limiting payoff possibilities set and rely on a fixed point theorem