  Social learning is learning through the observation of or interaction with
other individuals; it is critical in the understanding of the collective
behaviors of humans in social physics. We study the learning process of agents
in a restless multiarmed bandit (rMAB). The binary payoff of each arm changes
randomly and agents maximize their payoffs by exploiting an arm with payoff 1,
searching the arm at random (individual learning), or copying an arm exploited
by other agents (social learning). The system has Pareto and Nash equilibria in
the mixed strategy space of social and individual learning. We study several
models in which agents maximize their expected payoffs in the strategy space,
and demonstrate analytically and numerically that the system converges to the
equilibria. We also conducted an experiment and investigated whether human
participants adopt the optimal strategy. In this experiment, three participants
play the game. If the reward of each group is proportional to the sum of the
payoffs, the median of the social learning rate almost coincides with that of
the Pareto equilibrium.
