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Mathematics > Dynamical Systems
Title: Limiting dynamics for Q-learning with memory one in symmetric two-player, two-action games
(Submitted on 29 Jul 2021 (v1), last revised 3 Oct 2022 (this version, v2))
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.
Submission history
From: Janusz Meylahn [view email][v1] Thu, 29 Jul 2021 14:13:48 GMT (334kb,D)
[v2] Mon, 3 Oct 2022 13:38:02 GMT (22192kb,D)
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