The Bactra Review Individual
Strategy and Social Structure
In particular, his models show ergodicity. Basically, this means that if you
have a large number of such systems, and at any one time p percent of
them are in a given state, then every single one of them will spend about
p percent of its time in that state. (Technically, there's a
distribution over the states such that the state-space average of any
well-behaved function equals its time-average starting from almost any state,
if you take the latter over a long enough interval.) Ergodicity is a very
strong property, and one of the stronger predictions his models make; it goes
away if the agents are not perverse, or can remember unlimited stretches of the
past, in which case each population will lock in to a single convention
forever. It is also liable to be hard to test empirically, because it can take
a considerable time to converge on the ergodic distribution, and in the
meanwhile the game people are playing is apt to have changed.