Convexity of oligopoly games without transferable technologies

We present sufficient conditions involving the inverse demand function and the cost functions to establish the convexity of oligopoly TU-games without transferable technologies. For convex TU-games it is well known that the core is relatively large and that it is generically nonempty. The former property provides us with an answer about the stability of cartels, the latter property gives us an indication about the incentive to found a cartel. Furthermore, for convex games the kernel is a singleton in the core and the Shapley value is located in the center of gravity of the core, thus, there are natural solutions available to split the benefits of a cartel agreement.