Abstract. The single-agent multi-armed bandit problem can be solved by an agent that learns the values of each action using reinforcement learning. However, the multi-agent version of the problem, the iterated normal form game, presents a more complex challenge, since the rewards available to each agent depend on the strategies of the others. We consider the behavior of valuebased learning agents in this situation, and show that such agents cannot generally play at a Nash equilibrium, although if smooth best responses are used, a Nash distribution can be reached. We introduce a particular value-based learning algorithm, which we call individual Q-learning, and use stochastic approximation to study the asymptotic behavior, showing that strategies will converge to Nash distribution almost surely in 2-player zero-sum games and 2-player partnership games. Playerdependent learning rates are then considered, and it is shown that this extension converges in some games for which many algorithms, including the basic algorithm initially considered, fail to converge.
When the evaluation of the Q-values is totally indepen-dent, as in the individual Q-learning in REF , then convergence to Nash equilibria has been shown only for 2player zero-sum games and 2-player partnership games with countably many Nash equilibria.
Individual Q-learning in normal form games
In submission
Mathematics Computer Science