  Evolutionary dynamics provides an iconic relationship --- the periodic
frequency of a game is determined by the payoff matrix of the game. This paper
reports the first experimental evidence to demonstrate this relationship.
Evidence comes from two populations randomly-matched $2\times2$ games with 12
different payoff matrix parameters. The directions, frequencies and changes in
the radius of the cycles are measured definitively. The main finding is that
the observed periodic frequencies of the persistent cycles are significantly
different in games with different parameters. Two replicator dynamics, standard
and adjusted, are employed as predictors for the periodic frequency.
Interestingly, both of the models could infer the difference of the observed
frequencies well. The experimental frequencies linearly, positively and
significantly relate to the theoretical frequencies, but the adjusted model
performs slightly better.
