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arXiv · 2107.13995

Limiting dynamics for Q-learning with memory one in symmetric two-player, two-action games

Janusz M Meylahn·Lars Janssen
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Abstract

We develop a method based on computer algebra systems to represent the mutual pure strategy best-response dynamics of symmetric two-player, two-action repeated games played by players with a one-period memory. We apply this method to the iterated prisoner's dilemma, stag hunt and hawk-dove games and identify all possible equilibrium strategy pairs and the conditions for their existence. The only equilibrium strategy pair that is possible in all three games is the win-stay, lose-shift strategy. Lastly, we show that the mutual best-response dynamics are realized by a sample batch Q-learning algorithm in the infinite batch size limit.

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Janusz M Meylahn, Lars Janssen. 2021-07-29. Limiting dynamics for Q-learning with memory one in symmetric two-player, two-action games. https://arxiv.org/abs/2107.13995

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