Games of bounded deviation,additivizations of games and asymptotic martingales

We consider games in coalition function form on a, generally infinite, algebra of coalitions. For finite algebras the additive part mappingv E(v ¦) is the usual. The concern here is the analogue for infinite algebras. The useful construction is the finitely additive stochastic process of additive parts of the game on the filtration _f of finite subalgebras of.It is shown that is an isomorphism between:

a)	Additive games and martingales
b)	Superadditive games and supermartingales
c)	Shapley's games of bounded deviationBD() in his (1953) dissertation and bounded F-processes of Armstrong (1983)
d)	Gilboa's spaceBS() (1989) and bounded processes of Armstrong (1983)