# Multiplayer Performative Prediction: Learning in Decision-Dependent Games

arXiv: https://arxiv.org/abs/2201.03398 · HTML: https://mlsanity.com/paper/2201.03398/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 53 references that are in the map.
- First posted on arXiv 10 Jan 2022.

## Builds on (most cited first, 23 of 23)

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [DeltaGrad: Rapid retraining of machine learning models](https://mlsanity.com/paper/2006.14755/) (2020)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization](https://mlsanity.com/paper/1506.08272/) (2015)
- [Runaway Feedback Loops in Predictive Policing](https://mlsanity.com/paper/1706.09847/) (2017)
- [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)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [Learning in games with continuous action sets and unknown payoff functions](https://mlsanity.com/paper/1608.07310/) (2016)
- [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)
- [Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression](https://mlsanity.com/paper/1602.05419/) (2016)
- [State Dependent Performative Prediction with Stochastic Approximation](https://mlsanity.com/paper/2110.00800/) (2021)
- [Bandit learning in concave N-person games](https://mlsanity.com/paper/1810.01925/) (2018)
- [Continual Learning in Practice](https://mlsanity.com/paper/1903.05202/) (2019)
- [On the Characterization of Local Nash Equilibria in Continuous Games](https://mlsanity.com/paper/1411.2168/) (2014)
- [Online Projected Gradient Descent for Stochastic Optimization with Decision-Dependent Distributions](https://mlsanity.com/paper/2107.09721/) (2021)
- [Gaming Helps! Learning from Strategic Interactions in Natural Dynamics](https://mlsanity.com/paper/2002.07024/) (2020)
- [Learning Nash Equilibria in Monotone Games](https://mlsanity.com/paper/1904.01882/) (2019)
- [Improved Rates for Derivative Free Gradient Play in Strongly Monotone Games](https://mlsanity.com/paper/2111.09456/) (2021)
- [Convergence Analysis of Gradient-Based Learning with Non-Uniform Learning Rates in Non-Cooperative Multi-Agent Settings](https://mlsanity.com/paper/1906.00731/) (2019)

## Built on by (most cited first, 30 of 44)

- [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)
- [Multi-agent Performative Prediction: From Global Stability and Optimality to Chaos](https://mlsanity.com/paper/2201.10483/) (2022)
- [Making Decisions under Outcome Performativity](https://mlsanity.com/paper/2210.01745/) (2022)
- [Performative Reinforcement Learning](https://mlsanity.com/paper/2207.00046/) (2022)
- [Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts](https://mlsanity.com/paper/2305.05090/) (2023)
- [Performative Reinforcement Learning in Gradually Shifting Environments](https://mlsanity.com/paper/2402.09838/) (2024)
- [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)
- [Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instruments](https://mlsanity.com/paper/2208.11040/) (2022)
- [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)
- [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)
- [Clipped SGD Algorithms for Performative Prediction: Tight Bounds for Clipping Bias and Remedies](https://mlsanity.com/paper/2404.10995/) (2024)
- [Independent Learning in Performative Markov Potential Games](https://mlsanity.com/paper/2504.20593/) (2025)
- [Tight Lower Bounds and Improved Convergence in Performative Prediction](https://mlsanity.com/paper/2412.03671/) (2024)
- [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)
- [Policy Design for Two-sided Platforms with Participation Dynamics](https://mlsanity.com/paper/2502.01792/) (2025)
- [Nonlinear Performative Prediction](https://mlsanity.com/paper/2509.01139/) (2025)
- [Look-Ahead Reasoning on Learning Platforms](https://mlsanity.com/paper/2511.14745/) (2025)
- [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)
- [Partially Performative Prediction](https://mlsanity.com/paper/2606.07890/) (2026)

## Abstract (arXiv)

Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player performative prediction". We focus on two distinct solution concepts, namely (i) performatively stable equilibria and (ii) Nash equilibria of the game. The latter equilibria are arguably more informative, but can be found efficiently only when the game is monotone. We show that under mild assumptions, the performatively stable equilibria can be found efficiently by a variety of algorithms, including repeated retraining and the repeated (stochastic) gradient method. We then establish transparent sufficient conditions for strong monotonicity of the game and use them to develop algorithms for finding Nash equilibria. We investigate derivative free methods and adaptive gradient algorithms wherein each player alternates between learning a parametric description of their distribution and gradient steps on the empirical risk. Synthetic and semi-synthetic numerical experiments illustrate the results.