This paper presents a learning process which is a generalization of the method of fictitious play of Brown. If the learning process converges, the convergence point is a Nash equilibrium. We study 2 × 2 games. Here the process always converges. The relation between the initial prior, the weight assigned to this prior, and the equilibrium selected is examined. As the weight increases, the relation between the prior and the equilibrium selected becomes almost identical to that of the tracing procedure of Harsanyi. In this way the learning process supports the concept of risk dominance of Harsanyi and Selten