Abstract:

Within this series of papers we plan to exhibit to any noncooperative game in strategic or normal form a 'canonical' representation in extensive form that preserves all symmetries of the game. The operation defined this way will respect the restriction of games to subgames and yield a minimal total rank of the tree involved. Moreover, by the above requirements the 'canonical extensive game form' will be uniquely defined. Part I is dealing with isomorphisms of game forms and games. An auto- morphism of the game is called motion. A symmetry of a game is a permuta- tion which can be augmented to a motion. Some results on the existence of symmetry groups are presented. The context to the notion of symmetry for coalitional games is exhibited.

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