  Evolutionary game theory assumes that players replicate a highly scored
player's strategy through genetic inheritance. However, when learning occurs
culturally, it is often difficult to recognize someone's strategy just by
observing the behaviour. In this work, we consider players with memory-one
stochastic strategies in the iterated prisoner's dilemma, with an assumption
that they cannot directly access each other's strategy but only observe the
actual moves for a certain number of rounds. Based on the observation, the
observer has to infer the resident strategy in a Bayesian way and chooses his
or her own strategy accordingly. By examining the best-response relations, we
argue that players can escape from full defection into a cooperative
equilibrium supported by Win-Stay-Lose-Shift in a self-confirming manner,
provided that the cost of cooperation is low and the observational learning
supplies sufficiently large uncertainty.
