Cores of $3$-distant convex games

Convex cooperative games have a nonempty core and admit an efficient construction of core allocations. However, economically natural local frictions may violate convexity. We study the core of $3$-distant convex games, which permit violations of convexity only between closely related coalitions. Although the core of such a game may be empty, we establish a simple necessary and sufficient condition for its nonemptiness. We also develop a strongly polynomial-time combinatorial algorithm for finding a core allocation whenever one exists. Finally, we demonstrate the applicability of the framework to oligopolistic competition with merger synergies and profit allocation of joint production with complementary inputs.