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In the rapidly evolving landscape of eCommerce, Artificial Intelligence (AI) based pricing algorithms, particularly those utilizing Reinforcement Learning (RL), are becoming increasingly prevalent. This rise has led to an inextricable…

Machine Learning · Computer Science 2024-06-06 Michael Schlechtinger , Damaris Kosack , Franz Krause , Heiko Paulheim

Nowadays, a significant share of the Business-to-Consumer sector is based on online platforms like Amazon and Alibaba and uses Artificial Intelligence for pricing strategies. This has sparked debate on whether pricing algorithms may tacitly…

General Economics · Economics 2024-06-05 Shidi Deng , Maximilian Schiffer , Martin Bichler

Artificial intelligence algorithms are increasingly used by firms to set prices. Previous research shows that they can exhibit collusive behaviour, but how quickly they can do so has so far remained an open question. I show that a modern…

General Economics · Economics 2026-04-20 Kevin Michael Frick

Pricing algorithms have demonstrated the capability to learn tacit collusion that is largely unaddressed by current regulations. Their increasing use in markets, including oligopolistic industries with a history of collusion, calls for…

Computer Science and Game Theory · Computer Science 2025-02-26 Paul Friedrich , Barna Pásztor , Giorgia Ramponi

Nowadays, a significant share of the business-to-consumer sector is based on online platforms like Amazon and Alibaba and uses AI for pricing strategies. This has sparked debate on whether pricing algorithms may tacitly collude to set…

General Economics · Economics 2025-03-17 Shidi Deng , Maximilian Schiffer , Martin Bichler

The rise of algorithmic pricing in online retail platforms has attracted significant interest in how autonomous software agents interact under competition. This article explores the potential emergence of algorithmic collusion -…

Computer Science and Game Theory · Computer Science 2025-04-24 Martin Bichler , Julius Durmann , Matthias Oberlechner

This paper develops a formal framework to assess policies of learning algorithms in economic games. We investigate whether reinforcement-learning agents with collusive pricing policies can successfully extrapolate collusive behavior from…

General Economics · Economics 2022-01-06 Nicolas Eschenbaum , Filip Mellgren , Philipp Zahn

We develop a model of algorithmic pricing that shuts down every channel for explicit or implicit collusion while still generating collusive outcomes. We analyze the dynamics of a duopoly market where both firms use pricing algorithms…

Theoretical Economics · Economics 2024-03-13 Inkoo Cho , Noah Williams

Autonomous pricing algorithms are increasingly influencing competition in digital markets; however, their behavior under realistic demand conditions remains largely unexamined. This paper offers a thorough analysis of four pricing…

Machine Learning · Computer Science 2025-12-03 Aheer Sravon , Md. Ibrahim , Devdyuti Mazumder , Ridwan Al Aziz

Collusion in market pricing is a concept associated with human actions to raise market prices through artificially limited supply. Recently, the idea of algorithmic collusion was put forward, where the human action in the pricing process is…

Theoretical Economics · Economics 2025-01-29 Suzie Grondin , Arthur Charpentier , Philipp Ratz

Two issues of algorithmic collusion are addressed in this paper. First, we show that in a general class of symmetric games, including Prisoner's Dilemma, Bertrand competition, and any (nonlinear) mixture of first and second price auction,…

Theoretical Economics · Economics 2024-09-05 Zhang Xu , Wei Zhao

Reinforcement learning (RL) has re-emerged as a natural approach for training interactive LLM agents in real-world environments. However, directly applying the widely used Group Relative Policy Optimization (GRPO) algorithm to multi-turn…

Machine Learning · Computer Science 2026-01-27 Junbo Li , Peng Zhou , Rui Meng , Meet P. Vadera , Lihong Li , Yang Li

Deep Reinforcement Learning (DRL) algorithms often require a large amount of data and struggle in sparse-reward domains with long planning horizons and multiple sub-goals. In this paper, we propose a neuro-symbolic extension of Proximal…

Artificial Intelligence · Computer Science 2026-04-29 Simone Murari , Celeste Veronese , Daniele Meli

Proximal policy optimization (PPO) is one of the most popular state-of-the-art on-policy algorithms that has become a standard baseline in modern reinforcement learning with applications in numerous fields. Though it delivers stable…

Machine Learning · Computer Science 2025-02-25 Qisai Liu , Zhanhong Jiang , Hsin-Jung Yang , Mahsa Khosravi , Joshua R. Waite , Soumik Sarkar

Offline reinforcement learning (RL) is a challenging setting where existing off-policy actor-critic methods perform poorly due to the overestimation of out-of-distribution state-action pairs. Thus, various additional augmentations are…

Machine Learning · Computer Science 2023-02-23 Zifeng Zhuang , Kun Lei , Jinxin Liu , Donglin Wang , Yilang Guo

Instability and slowness are two main problems in deep reinforcement learning. Even if proximal policy optimization (PPO) is the state of the art, it still suffers from these two problems. We introduce an improved algorithm based on…

Machine Learning · Computer Science 2019-10-01 Zhenyu Zhang , Xiangfeng Luo , Tong Liu , Shaorong Xie , Jianshu Wang , Wei Wang , Yang Li , Yan Peng

Proximal Policy Optimization (PPO) is among the most widely used deep reinforcement learning algorithms, yet its theoretical foundations remain incomplete. Most importantly, convergence and understanding of fundamental PPO advantages remain…

Machine Learning · Computer Science 2026-02-04 Leif Doering , Daniel Schmidt , Moritz Melcher , Sebastian Kassing , Benedikt Wille , Tilman Aach , Simon Weissmann

Reinforcement learning (RL) is attracting increasing interests in autonomous driving due to its potential to solve complex classification and control problems. However, existing RL algorithms are rarely applied to real vehicles for two…

Machine Learning · Computer Science 2020-03-04 Lu Wen , Jingliang Duan , Shengbo Eben Li , Shaobing Xu , Huei Peng

Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO) are among the most successful policy gradient approaches in deep reinforcement learning (RL). While these methods achieve state-of-the-art performance across a…

Machine Learning · Computer Science 2020-06-22 Ahmed Touati , Amy Zhang , Joelle Pineau , Pascal Vincent

Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO), as the widely employed policy based reinforcement learning (RL) methods, are prone to converge to a sub-optimal solution as they limit the policy representation…

Machine Learning · Computer Science 2020-06-16 Jun Song , Chaoyue Zhao
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