## 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 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, 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. 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.

Translated title of the contribution | Individual Q-learning in normal form games |
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Original language | English |

Pages (from-to) | 495 - 514 |

Number of pages | 20 |

Journal | SIAM Journal on Control and Optimization |

Volume | 44 (2) |

DOIs | |

Publication status | Published - Mar 2005 |

### Bibliographical note

Publisher: Society for Industrial and Applied MathematicsOther identifier: IDS Number: 966OB

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