Formalization Of Multi-Level Games

The article presents multilevel game theory, as a generalization of conventional single-level game theory as it has developed since von Neumann and Morgenstern (1944). We define a multilevel game structure, multilevel games, payoffs and distribution rules, upward feasible strategies and the solution concept multilevel Nash equilibrium (MNE) in such games. A MNE must be, for each player, a best reply against itself with respect to alternative strategies that may have other players deviate as well, in contrast to the NE for conventional games where simultaneous deviations by more than one player are not considered. Although every pure or mixed MNE must give the same outcome as a NE of the extensive form representation, a NE is not necessarily a MNE. It is shown that a MNE need not exist in pure or mixed strategies and, if it does, it may not be unique. In the former case, the multilevel structure is considered unmaintainable.