# Multi-agent Performative Prediction with Greedy Deployment and Consensus Seeking Agents

arXiv: https://arxiv.org/abs/2209.03811 · HTML: https://mlsanity.com/paper/2209.03811/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2022.

## Built on by (most cited first, 23 of 23)

- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [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)
- [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)
- [Performative Reinforcement Learning with Linear Markov Decision Process](https://mlsanity.com/paper/2411.05234/) (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)
- [Performative Policy Gradient: Optimality in Performative Reinforcement Learning](https://mlsanity.com/paper/2512.20576/) (2025)
- [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)
- [The Stability of Online Algorithms in Performative Prediction](https://mlsanity.com/paper/2602.24207/) (2026)
- [Learning from Streaming Data when Users Choose](https://mlsanity.com/paper/2406.01481/) (2024)
- [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)
- [Optimal Regularization for Performative Learning](https://mlsanity.com/paper/2510.12249/) (2025)
- [Adjusting Pretrained Backbones for Performativity](https://mlsanity.com/paper/2410.04499/) (2024)
- [Asynchronous and Stochastic Distributed Resource Allocation](https://mlsanity.com/paper/2509.01172/) (2025)
- [Towards Performatively Stable Equilibria in Decision-Dependent Games for Arbitrary Data Distribution Maps](https://mlsanity.com/paper/2509.02619/) (2025)
- [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026)
- [Performative Learning Theory](https://mlsanity.com/paper/2602.04402/) (2026)
- [Stabilizing Performative Feedback Loops with Minimal Model Deployments](https://mlsanity.com/paper/2609.14065/) (2026)

## Abstract (arXiv)

We consider a scenario where multiple agents are learning a common decision vector from data which can be influenced by the agents' decisions. This leads to the problem of multi-agent performative prediction (Multi-PfD). In this paper, we formulate Multi-PfD as a decentralized optimization problem that minimizes a sum of loss functions, where each loss function is based on a distribution influenced by the local decision vector. We first prove the necessary and sufficient condition for the Multi-PfD problem to admit a unique multi-agent performative stable (Multi-PS) solution. We show that enforcing consensus leads to a laxer condition for the existence of Multi-PS solution with respect to the distributions' sensitivities, compared to the single agent case. Then, we study a decentralized extension to the greedy deployment scheme [Mendler-D"unner et al., 2020], called the DSGD-GD scheme. We show that DSGD-GD converges to the Multi-PS solution and analyze its non-asymptotic convergence rate. Numerical results validate our analysis.