# Markets with Heterogeneous Agents: Dynamics and Survival of Bayesian vs. No-Regret Learners

arXiv: https://arxiv.org/abs/2502.08597 · HTML: https://mlsanity.com/paper/2502.08597/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 89 references that are in the map.
- First posted on arXiv 12 Feb 2025.

## Builds on (most cited first, 30 of 33)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Selling to a No-Regret Buyer](https://mlsanity.com/paper/1711.09176/) (2017)
- [The Sample Complexity of Online Contract Design](https://mlsanity.com/paper/2211.05732/) (2022)
- [Strategizing against Learners in Bayesian Games](https://mlsanity.com/paper/2205.08562/) (2022)
- [Bilateral Trade: A Regret Minimization Perspective](https://mlsanity.com/paper/2109.12974/) (2021)
- [Learning in Auctions: Regret is Hard, Envy is Easy](https://mlsanity.com/paper/1511.01411/) (2015)
- [Contracting with a Learning Agent](https://mlsanity.com/paper/2401.16198/) (2024)
- [Auctions Between Regret-Minimizing Agents](https://mlsanity.com/paper/2110.11855/) (2021)
- [Autobidders with Budget and ROI Constraints: Efficiency, Regret, and Pacing Dynamics](https://mlsanity.com/paper/2301.13306/) (2023)
- [A Regret Analysis of Bilateral Trade](https://mlsanity.com/paper/2102.08754/) (2021)
- [Selling to Multiple No-Regret Buyers](https://mlsanity.com/paper/2307.04175/) (2023)
- [How and Why to Manipulate Your Own Agent: On the Incentives of Users of Learning Agents](https://mlsanity.com/paper/2112.07640/) (2021)
- [Pareto-Optimal Algorithms for Learning in Games](https://mlsanity.com/paper/2402.09549/) (2024)
- [Convergence Analysis of No-Regret Bidding Algorithms in Repeated Auctions](https://mlsanity.com/paper/2009.06136/) (2020)
- [Regulation of Algorithmic Collusion](https://mlsanity.com/paper/2401.15794/) (2024)
- [Nash Convergence of Mean-Based Learning Algorithms in First-Price Auctions](https://mlsanity.com/paper/2110.03906/) (2021)
- [Regulation of Algorithmic Collusion, Refined: Testing Pessimistic Calibrated Regret](https://mlsanity.com/paper/2501.09740/) (2025)
- [No-Regret Learning in Partially-Informed Auctions](https://mlsanity.com/paper/2202.10606/) (2022)
- [Algorithmic Collusion Without Threats](https://mlsanity.com/paper/2409.03956/) (2024)
- [Liquid Welfare Guarantees for No-Regret Learning in Sequential Budgeted Auctions](https://mlsanity.com/paper/2210.07502/) (2022)
- [Optimal Collaterals in Multi-Enterprise Investment Networks](https://mlsanity.com/paper/2011.06247/) (2020)
- [Repeated Contracting with Multiple Non-Myopic Agents: Policy Regret and Limited Liability](https://mlsanity.com/paper/2402.17108/) (2024)
- [Dynamics of Distributed Updating in Fisher Markets](https://mlsanity.com/paper/1806.04746/) (2018)
- [Strategic Budget Selection in a Competitive Autobidding World](https://mlsanity.com/paper/2307.07374/) (2023)
- [On the Convergence of Learning Algorithms in Bayesian Auction Games](https://mlsanity.com/paper/2311.15398/) (2023)
- [Games with Payments between Learning Agents](https://mlsanity.com/paper/2405.20880/) (2024)
- [Learning to Play Against Unknown Opponents](https://mlsanity.com/paper/2412.18297/) (2024)
- [Learning in Budgeted Auctions with Spacing Objectives](https://mlsanity.com/paper/2411.04843/) (2024)
- [Universal Growth in Production Economies](https://mlsanity.com/paper/1802.07385/) (2018)

## Built on by (most cited first, 1 of 1)

- [From No-Regret to Strategically Robust Learning in Repeated Auctions](https://mlsanity.com/paper/2601.03853/) (2026)

## Abstract (arXiv)

We analyze the performance of heterogeneous learning agents in asset markets with stochastic payoffs. Our main focus is on comparing Bayesian learners and no-regret learners who compete in markets and identifying the conditions under which each approach is more effective. We formally relate the notions of survival and market dominance studied in economics and the framework of regret minimization, thereby bridging these theories. A central finding is that regret plays a key role in market selection, but low regret alone does not guarantee survival: surprisingly, an agent may achieve even logarithmic regret and yet be driven out of the market when competing against a Bayesian learner with a finite prior that assigns positive probability to the correct model. At the same time, we show that Bayesian learning is highly fragile, while no-regret learning requires less knowledge of the environment and is therefore more robust. Motivated by this contrast, we propose two simple hybrid strategies that incorporate Bayesian updates while improving robustness and adaptability to distribution shifts, taking a step toward a best-of-both-worlds learning approach. More broadly, our work contributes to the understanding of dynamics of heterogeneous learning agents and their impact on markets.