The core consists of efficient payoff vectors for which each coalition receives at least its own attainable value. Thus no coalition can improve every member's payoff by leaving. It is a convex set defined by linear constraints, but can be empty. Every convex cooperative game has a nonempty core because each marginal contribution vector belongs to it.
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In game theory, the "core" is a concept that refers to a specific solution concept associated with cooperative games. A cooperative game is one in which players can form binding agreements and coalitions to improve their outcomes. The core is a set of achievable allocations of resources or payoffs to players that cannot be improved upon by any coalition of players.