Multiagent reinforcement learning in the Iterated Prisoner's Dilemma

Abstract

Reinforcement learning (RL) is based on the idea that the tendency to produce an action should be strengthened (reinforced) if it produces favorable results, and weakened if it produces unfavorable results. Q-learning is a recent RL algorithm that does not need a model of its environment and can be used on-line. Therefore, it is well suited for use in repeated games against an unknown opponent. Most RL research has been confined to single-agent settings or to multiagent settings where the agents have totally positively correlated payoffs (team problems) or totally negatively correlated payoffs (zero-sum games). This paper is an empirical study of reinforcement learning in the Iterated Prisoner's Dilemma (IPD), where the agents' payoffs are neither totally positively nor totally negatively correlated. RL is considerably more difficult in such a domain. This paper investigates the ability of a variety of Q-learning agents to play the IPD game against an unknown opponent. In some experiments, the opponent is the fixed strategy Tit-For-Tat, while in others it is another Q-learner. All the Q-learners learned to play optimally against Tit-For-Tat. Playing against another learner was more difficult because the adaptation of the other learner created a non-stationary environment, and because the other learner was not endowed with any a priori knowledge about the IPD game such as a policy designed to encourage cooperation. The learners that were studied varied along three dimensions: the length of history they received as context, the type of memory they employed (lookup tables based on restricted history windows or recurrent neural networks that can theoretically store features from arbitrarily deep in the past), and the exploration schedule they followed. Although all the learners faced difficulties when playing against other learners, agents with longer history windows, lookup table memories, and longer exploration schedules fared best in the IPD games.