The seeming diversity of the fields above disappears when seen from a sufficiently global perspective. In fact, these fields all employ the decision tree optimization methods formalized by von Neumann and Morgenstern in 1944. These methods require strategically interacting players to adopt a single type of joint probability measure space defining separable joint probability distributions allowing the analysis of every possible combination of strategic moves on a single decision tree. In contrast, Kae Nemoto and I suggest that players optimize strategic outcomes by first choosing between different joint probability measure spaces each of which alters the probability distributions governing optimal move selection to generate novel optimal equilibria..

That is, we consider a strategic interaction where players X and Y seek to optimize their expected payoffs <Π^X> and <Π^Y> and where X chooses event x and Y chooses event y to generate respective payoffs of Π^X(x,y) and Π^Y(x,y). The chosen events x×y are contained in Ω^X×Ω^Y, the set of all possible events in the game and in both player's chosen "roulette" randomization devices. These devices are used by players to avoid their choices being forecast and exploited, with the result that the choice of events is described using a joint probability measure dP^XY_xy. The definition of this measure requires players X and Y to adopt respective probability measure spaces P^X and P^Y able to support the required measure. We allow players to vary their choice of probability measure space to maximize their expected payoffs. Altogether, the joint optimization task is

Our generalized methods will impact on game theory and strategic economics, the minimax search algorithm of artificial intelligence, and approaches to complex systems theory and the understanding of the evolution and dynamics of complex biological systems including life, intelligence, and consciousness.

See "Variational optimization of probability measure spaces resolves the chain store paradox", M. J. Gagen and K. Nemoto, Eprint Archive:math.CO/0604611 (2006)