# Multi-agent Performative Prediction: From Global Stability and Optimality to Chaos

arXiv: https://arxiv.org/abs/2201.10483 · HTML: https://mlsanity.com/paper/2201.10483/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 63 references that are in the map.
- First posted on arXiv 25 Jan 2022.

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

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [No-regret learning and mixed Nash equilibria: They do not mix](https://mlsanity.com/paper/2010.09514/) (2020)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Multiplicative Weights Update with Constant Step-Size in Congestion Games: Convergence, Limit Cycles and Chaos](https://mlsanity.com/paper/1703.01138/) (2017)
- [Survival of the strictest: Stable and unstable equilibria under regularized learning with partial information](https://mlsanity.com/paper/2101.04667/) (2021)
- [On the Impossibility of Global Convergence in Multi-Loss Optimization](https://mlsanity.com/paper/2005.12649/) (2020)
- [Chaos, Extremism and Optimism: Volume Analysis of Learning in Games](https://mlsanity.com/paper/2005.13996/) (2020)
- [The route to chaos in routing games: When is Price of Anarchy too optimistic?](https://mlsanity.com/paper/1906.02486/) (2019)
- [Learning in Matrix Games can be Arbitrarily Complex](https://mlsanity.com/paper/2103.03405/) (2021)
- [Follow-the-Regularized-Leader Routes to Chaos in Routing Games](https://mlsanity.com/paper/2102.07974/) (2021)
- [Chaos of Learning Beyond Zero-sum and Coordination via Game Decompositions](https://mlsanity.com/paper/2008.00540/) (2020)
- [Learning and Strongly Truthful Multi-Task Peer Prediction: A Variational Approach](https://mlsanity.com/paper/2009.14730/) (2020)
- [Multiplicative Weights Update as a Distributed Constrained Optimization Algorithm: Convergence to Second-order Stationary Points Almost Always](https://mlsanity.com/paper/1810.05355/) (2018)
- [Smooth markets: A basic mechanism for organizing gradient-based learners](https://mlsanity.com/paper/2001.04678/) (2020)
- [The Limits of Multi-task Peer Prediction](https://mlsanity.com/paper/2106.03176/) (2021)
- [Optimal Scoring Rule Design under Partial Knowledge](https://mlsanity.com/paper/2107.07420/) (2021)
- [Limitations of Greed: Influence Maximization in Undirected Networks Re-visited](https://mlsanity.com/paper/2002.11679/) (2020)
- [Dynamical Analysis of the EIP-1559 Ethereum Fee Market](https://mlsanity.com/paper/2102.10567/) (2021)
- [Subspace Differential Privacy](https://mlsanity.com/paper/2108.11527/) (2021)
- [Learning in Markets: Greed Leads to Chaos but Following the Price is Right](https://mlsanity.com/paper/2103.08529/) (2021)
- [Cooperation in Threshold Public Projects with Binary Actions](https://mlsanity.com/paper/2105.08572/) (2021)
- [Think Globally, Act Locally: On the Optimal Seeding for Nonsubmodular Influence Maximization](https://mlsanity.com/paper/2003.10393/) (2020)
- [Timely Information from Prediction Markets](https://mlsanity.com/paper/2011.03645/) (2020)
- [Consensus Multiplicative Weights Update: Learning to Learn using Projector-based Game Signatures](https://mlsanity.com/paper/2106.02615/) (2021)

## Built on by (most cited first, 30 of 33)

- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [Anticipating Performativity by Predicting from Predictions](https://mlsanity.com/paper/2208.07331/) (2022)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality](https://mlsanity.com/paper/2207.04173/) (2022)
- [Performative Prediction with Bandit Feedback: Learning through Reparameterization](https://mlsanity.com/paper/2305.01094/) (2023)
- [Zero-Regret Performative Prediction Under Inequality Constraints](https://mlsanity.com/paper/2309.12618/) (2023)
- [Designing Long-term Group Fair Policies in Dynamical Systems](https://mlsanity.com/paper/2311.12447/) (2023)
- [Performative Reinforcement Learning with Linear Markov Decision Process](https://mlsanity.com/paper/2411.05234/) (2024)
- [The Good, the Bad, and the Hulk-like GPT: Analyzing Emotional Decisions of Large Language Models in Cooperation and Bargaining Games](https://mlsanity.com/paper/2406.03299/) (2024)
- [Performative Prediction on Games and Mechanism Design](https://mlsanity.com/paper/2408.05146/) (2024)
- [Decision-Dependent Stochastic Optimization: The Role of Distribution Dynamics](https://mlsanity.com/paper/2503.07324/) (2025)
- [On Corruption-Robustness in Performative Reinforcement Learning](https://mlsanity.com/paper/2505.05609/) (2025)
- [Performative Policy Gradient: Optimality in Performative Reinforcement Learning](https://mlsanity.com/paper/2512.20576/) (2025)
- [Emergent specialization from participation dynamics and multi-learner retraining](https://mlsanity.com/paper/2206.02667/) (2022)
- [Independent Learning in Performative Markov Potential Games](https://mlsanity.com/paper/2504.20593/) (2025)
- [The Stability of Online Algorithms in Performative Prediction](https://mlsanity.com/paper/2602.24207/) (2026)
- [Strategic Usage in a Multi-Learner Setting](https://mlsanity.com/paper/2401.16422/) (2024)
- [Identifying Predictions That Influence the Future: Detecting Performative Concept Drift in Data Streams](https://mlsanity.com/paper/2412.10545/) (2024)
- [Learning from Streaming Data when Users Choose](https://mlsanity.com/paper/2406.01481/) (2024)
- [Observations and Remedies for Large Language Model Bias in Self-Consuming Performative Loop](https://mlsanity.com/paper/2601.05184/) (2026)
- [On the Computational Complexity of Performative Prediction](https://mlsanity.com/paper/2601.20180/) (2026)
- [Dissecting Performative Prediction: A Comprehensive Survey](https://mlsanity.com/paper/2602.10176/) (2026)
- [When and How Human Curation Backfires: Preference Alignment under Multi-Model Self-Consuming Loop](https://mlsanity.com/paper/2605.29267/) (2026)
- [Tracking solutions of time-varying variational inequalities](https://mlsanity.com/paper/2406.14059/) (2024)
- [Swim till You Sink: Computing the Limit of a Game](https://mlsanity.com/paper/2408.11146/) (2024)
- [Chaos persists in large-scale multi-agent learning despite adaptive learning rates](https://mlsanity.com/paper/2306.01032/) (2023)
- [On multiagent online problems with predictions](https://mlsanity.com/paper/2507.12486/) (2025)
- [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026)
- [Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos](https://mlsanity.com/paper/2607.21805/) (2026)

## Abstract (arXiv)

The recent framework of performative prediction is aimed at capturing settings where predictions influence the target/outcome they want to predict. In this paper, we introduce a natural multi-agent version of this framework, where multiple decision makers try to predict the same outcome. We showcase that such competition can result in interesting phenomena by proving the possibility of phase transitions from stability to instability and eventually chaos. Specifically, we present settings of multi-agent performative prediction where under sufficient conditions their dynamics lead to global stability and optimality. In the opposite direction, when the agents are not sufficiently cautious in their learning/updates rates, we show that instability and in fact formal chaos is possible. We complement our theoretical predictions with simulations showcasing the predictive power of our results.