  In game theory, players have continuous expected payoff functions and can use
fixed point theorems to locate equilibria. This optimization method requires
that players adopt a particular type of probability measure space. Here, we
introduce alternate probability measure spaces altering the dimensionality,
continuity, and differentiability properties of what are now the game's
expected payoff functionals. Optimizing such functionals requires generalized
variational and functional optimization methods to locate novel equilibria.
These variational methods can reconcile game theoretic prediction and observed
human behaviours, as we illustrate by resolving the chain store paradox. Our
generalized optimization analysis has significant implications for economics,
artificial intelligence, complex system theory, neurobiology, and biological
evolution and development.
