The canonical extensive form of a game form: symmetries

Abstract

This paper is the first in a series of papers in which 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 automorphism of the game is called motion. A symmetry of a game is a permutation 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.