Nash equilibrium selection in multi-leader multi-follower games with vertical separation

The aim of this thesis is twofold. On the one hand new results on the concavity and the isotonicity of the optimal solution function of a parametric maximization problem are obtained. The maximizing function is not required to be continuous and the generalized version of the notion of pseudoconcavity in terms of Dini derivatives is used. These results, together with a new fixed point theorem for set-valued maps, are used to answer to the second issue concerning a selection of Nash equilibria, called equilibrium under passive beliefs, of a multi-leader multi-follower game with vertical separation and partially observed actions. Indeed, an equilibrium under passive beliefs correspond to a fixed point of particular set-valued maps related to the sets of solutions of parametric bilevel optimization problems. Existence of equilibria under passive beliefs for significative classes of problems and conditions of minimal character on data possibly discontinuous are proved. An economic example of such interaction can be found in games of multilateral vertical contracts: competing manufacturers (the leaders) delegate retail decisions to exclusive retailers (the followers), offering a private contract.