MULTISTAGE GAME MODELS AND DELAY SUPERGAMES

The order of stages in a multistage game is often interpreted by looki ng at earlier stages as involving more long term decisions. For the pu rpose of making this interpretation precise, the notion of a delay sup ergame of a bounded multistage game is introduced. A multistage game i s bounded if the length of play has an upper bound. A delay supergame is played over many periods. Decisions on all stages are made simultan eously, but with different delays until they become effective. The ear lier the stage the longer the delay. A subgame perfect equilibrium of a bounded multistage game generates a subgame perfect equilibrium in e very one of its delay supergames. This is the first main conclusion of the paper. A subgame perfect equilibrium set is a set of subgame perf ect equilibria all of which yield the same payoffs, not only in the ga me as a whole, but also in each of its subgames. The second main concl usion concerns multistage games with a unique subgame perfect equilibr ium set and their delay supergames which are bounded in the sense that the number of periods is finite. If a bounded multistage game has a u nique subgame perfect equilibrium set, then the same is true for every one of its bounded delay supergames. Finally the descriptive relevanc e of multistage game models and their subgame perfect equilibria is di scussed in the light of the results obtained.