A Q-learning approach to the Lowest Unique Positive Integer game
Keywords: Q-learning, Lowest Unique Positive Integer Game, Nash Equilibrium, Poisson-Nash equilibrium, real-time bidding, Swedish Limbo Lottery, multi-agent reinforcement learning, normal-form game, reverse auction, Poisson distribution, game theory. TL;DR: This paper introduces a Q-learning-based approach to solve the Lowest Unique Positive Integer game, outperforming traditional Poisson-based methods and demonstrating real-world applications such as in reverse auctions and real-time bidding systems
TL;DR: This paper introduces a Q-learning-based approach to solve the Lowest Unique Positive Integer game, outperforming traditional Poisson-based methods and demonstrating real-world applications such as in reverse auctions and real-time bidding systems.
Abstract: The Lowest Unique Positive Integer (LUPI) game is a multiplayer game where participants attempt to choose the smallest number that no one else selects. While previous studies model LUPI using Poisson--Nash equilibrium assumptions, our work introduces a novel Q-learning-based approach to achieve equilibrium without the need for specific distribution assumptions, such as Poisson. We demonstrate that our Q-learning model successfully emulates the Nash equilibrium while allowing flexibility in the number of players, providing a more robust and practical solution for real-world applications like real-time bidding (RTB) systems. We compare our model's performance against existing Poisson-based strategies, showcasing improved accuracy and adaptability. Furthermore, we apply our model to the Swedish Limbo lottery data and observe significant deviations from theoretical predictions, highlighting the strength of learning-based approaches in dynamic, real-world scenarios.
Primary Area: reinforcement learning
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Submission Number: 1392
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