Win-Stay-Lose-Shift as a self-confirming equilibrium in the iterated prisoner's dilemma

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.