This paper investigates potential game theoretic cooperative control. In particular, it focuses on payoff-based learning for potential games with a potential function equal to the formulated social welfare function. One of the authors' previous works on the topic provided a conjecture that taking irrational decisions in the payoff-based learning process is essential in achieving the potential function maximization. To reinforce the conjecture, the authors refine an algorithm, called simple experimentation, and present a novel payoff-based learning algorithm with irrational decisions. Then, the maximization is rigorously proved. The effectiveness of the present algorithm is finally demonstrated through simulation.