We examine the complexity of players in evolved populations of finite automata that play the iterated prisoners’ dilemma. We track the complexity of players measured bounding their Krohn-Rhodes complexity, a rigorous integer-valued mathematical measure from algebraic automata theory. In particular, we test Rhodes’ hypothesis that evolved organisms will attain a complexity approximately equal to their number of possible states. Results confirm that number of states in evolved populations are close to the complexity of the evolved automata if there is a cost to having more states and that the difference between complexity and number states is smaller when costs for states are higher.