The paper is devoted to two real problems that generate a cooperative game model with a so-called k-convex characteristic function when certain conditions are fulfilled. Both a bankruptcy problem and an information trading problem are modelled as a cooperative game by constructing the corresponding bankruptcy game as well as the information market game. Firstly, it is established that the bankruptcy game is a k-convex n-person game where 1•k•n-2 if and only if the estate is sufficient to meet the claims of creditors in any (n-k)-person coalition. Secondly, it is shown that the k-convexity property for the information market game is equivalent to the nonexistence of profits with respect to a restricted class of submarkets.
