This paper exhibits to any noncooperative game in strategic or normal form a 'canonical' game in extensive form that preserves all symmetries of the former one. The operation defined this way respects the restriction of games to subgames and yields a minimal total rank of the tree involved....

This paper constitutes the third part in a series dealing with vNM-Stable Sets, see J. Rosenmüller, "Convex vNM-Stable Sets for a Semi Orthogonal Game. Part I" [IMW Working Paper no. 483 (2013)], "Convex vNM-Stable Sets for a Semi Orthogonal Game. Part II" [IMW Working Paper no. 498 (2014)]. We...