(Average-) convexity of common pool and oligopoly TU-games (Q2772848)

The paper studies the convexity and average-convexity properties for a particular class of cooperative games, called common pool games. The common pool situation involves a cost function as well as an average joint production function. First, it is shown that if the relevant cost function is a linear function, then the common pool game are convex games. There are presented sufficient condition involving the cost functions and the average joint production function in order to guarantee the convexity of the common pool game. A similar approach is effective to investigate a relaxation of the convexity property known as the average-convexity property for a cooperative game. An example illustrates that oligopoly games are a special case of common pool games whenever the average joint production function represents an inverse demand function.