Perfect symmetry makes cooperative games pointless to negotiate. [causal]
The perfectly move-symmetrical cooperative game seems a little like that foot race. Bargaining in the one case is as unavailing as leg-work in the other; every player knows in advance that all moves and tactics are foredoomed to neutralization by the symmetrical potentialities available to his opponent. The interesting elements that we might inject in the bargaining game are meaningless if perfect symmetry, and its acceptance as inevitable by both players, are imposed on the game by its definition.
Thomas C. Schelling, The Strategy of Conflict, loc. 634