The topic is two-fold. First, we prove the convexity of Owen's Airport Profit Game (inclusive of revenues and costs). As an adjunct, we characterize the class of 1-convex Airport Profit Games by equivalent properties of the corresponding cost function. Second, we classify the class of 1-convex Bankruptcy Games by solving a minimization problem of its corresponding gap function.
A well-known result related to bankruptcy problems establishes that a vector is a bankruptcy allocation if and only if it belongs to the core of the associated O’Neill’s bankruptcy game. In this paper we show that this game is precisely the unique TU-game based on convex functions that satisfies the previous result. In addition, given a bankruptcy problem, we show a way for constructing bankruptcy games such that the set of bankruptcy allocations is a subset of their core or their core is a subset of the set of bankruptcy allocations. Also, we show how these results can be applied for finding new bankruptcy solutions.