Three Theorems on Non-Emptiness of Approximate Cores: Part 1. Game Theoretic Results
We introduce the framework of parametrized collections of games and provide three nonemptiness of approximate core theorems for arbitrary games without (and with) sidepayments. The framework and theorems are sufficiently general to encompass results in the literature on nonemptiness of approximate cores of games derived from pregames. The theorems are based on a new notion of strongly balanced profiles and approximately strongly balanced profiles.
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