Learning within a Markovian Environment

We investigate learning in a setting where each period a population has to choose between two actions and the payoff of each action is unknown by the players. The population learns according to reinforcement and the environment is non-stationary, meaning that there is correlation between the payoff of each action today and the payoff of each action in the past. We show that when players observe realized and foregone payoffs, a suboptimal mixed strategy is selected. On the other hand, when players only observe realized payoffs, a unique action, which is optimal if actions perform different enough, is selected in the long run. When looking for efficient reinforcement learning rules, we find that it is optimal to disregard the information from foregone payoffs and to learn as if only realized payoffs were observed.