Multistage game G with simultanous games Γ(·) played on each stage is considered. The definition of outcome, path in tree-graph and history are introduced.
The new class of Nash Solutions based on the possibilities of punishment for the deviation on first stages of G are defined. It is shown that the outcomes under these solutions dominate the classical subgame perfect Nash outcomes. For infinite multistage games G the regularization procedure is introduced which enables to construct a strong Nash Equilibrium (coalition-proof) in such class of games.