  Evolutionary game theory assumes that players replicate a highly scored
player's strategy through genetic inheritance, but in terms of cultural
learning, it is often difficult to recognize a 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 adjust his or her own
strategy accordingly. By examining 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.
