## Individual Q-learning in normal form games

Leslie, David , E. J. Collins
Individual Q-learning in normal form games
unpublished (PDF - 210K)

Abstract: The single-agent multi-armed bandit problem can be solved by an agent that learns the values of each action using reinforcement learning \cite{SuttonBarto98}. 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 behaviour of value-based 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, individual \$Q\$-learning, and use stochastic approximation to study the asymptotic behaviour, showing that strategies will converge to Nash distribution almost surely in 2-player zero-sum games and 2-player partnership games. Player-dependent 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.