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It is known that the complexity of the reinforcement learning algorithms, such as Q-learning, may be exponential in the number of environment's states. It was shown, however, that the learning complexity for the goal-directed problems may be substantially reduced by initializing the Q-values with a "good" approximative function. In the multiagent case, there exists such a good approximation for a big class of problems, namely, for goal-directed stochastic games. These games, for example, can reflect coordination and common interest problems of cooperative robotics. The approximative function for these games is nothing but the relaxed, singleagent, problem solution, which can easily be found by each agent individually. In this article, we show that (1) an optimal single-agent solution is a "good" approximation for the goal-directed stochastic games with action-penalty representation and (b) the complexity is reduced when the learning is initialized with this approximative function, as compared to the uninformed case.

Repeated games are an important mathematical formalism to model and study long-term economic interactions between multiple self-interested parties (individuals or groups of individuals). They open attractive perspectives in modeling long-term multiagent interactions. This overview paper discusses the most important results that actually exist for repeated games. These results arise from both economics and computer science. Contrary to a number of existing surveys of repeated games, most of which originated from the economic research community, we are first to pay a special attention to a number of important distinctive features proper to artificial agents. More precisely, artificial agents, as opposed to the human agents mainly aimed by the economic research, are usually bounded whether in terms of memory or performance. Therefore, their decisions have to be based on the strategies defined using finite representations. Furthermore, these strategies have to be efficiently computed or approximated using a limited computational resource usually available to artificial agents.

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