# Towards Performatively Stable Equilibria in Decision-Dependent Games for Arbitrary Data Distribution Maps

arXiv: https://arxiv.org/abs/2509.02619 · HTML: https://mlsanity.com/paper/2509.02619/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 53 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Builds on (most cited first, 26 of 26)

- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [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)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [Performative Prediction with Neural Networks](https://mlsanity.com/paper/2304.06879/) (2023)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [Performative Reinforcement Learning](https://mlsanity.com/paper/2207.00046/) (2022)
- [Multi-agent Performative Prediction with Greedy Deployment and Consensus Seeking Agents](https://mlsanity.com/paper/2209.03811/) (2022)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [Device Heterogeneity in Federated Learning: A Superquantile Approach](https://mlsanity.com/paper/2002.11223/) (2020)
- [Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts](https://mlsanity.com/paper/2305.05090/) (2023)
- [Stochastic Optimization Schemes for Performative Prediction with Nonconvex Loss](https://mlsanity.com/paper/2405.17922/) (2024)
- [Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality](https://mlsanity.com/paper/2207.04173/) (2022)
- [Performative Recommendation: Diversifying Content via Strategic Incentives](https://mlsanity.com/paper/2302.04336/) (2023)
- [Zero-Regret Performative Prediction Under Inequality Constraints](https://mlsanity.com/paper/2309.12618/) (2023)
- [Two-timescale Derivative Free Optimization for Performative Prediction with Markovian Data](https://mlsanity.com/paper/2310.05792/) (2023)
- [Performative Control for Linear Dynamical Systems](https://mlsanity.com/paper/2410.23251/) (2024)
- [Wasserstein Dropout](https://mlsanity.com/paper/2012.12687/) (2020)
- [A Generic Approach for Reproducible Model Distillation](https://mlsanity.com/paper/2211.12631/) (2022)
- [Performative Debias with Fair-exposure Optimization Driven by Strategic Agents in Recommender Systems](https://mlsanity.com/paper/2406.17475/) (2024)
- [Toward Finding Strong Pareto Optimal Policies in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2410.19372/) (2024)
- [Convex Optimization with an Interpolation-based Projection and its Application to Deep Learning](https://mlsanity.com/paper/2011.07016/) (2020)

## Abstract (arXiv)

In decision-dependent games, multiple players optimize their decisions under a data distribution that shifts with their joint actions, creating complex dynamics in applications like market pricing. A practical consequence of these dynamics is the textitperformatively stable equilibrium, where each player's strategy is a best response under the induced distribution. Prior work relies on β-smoothness, assuming Lipschitz continuity of loss function gradients with respect to the data distribution, which is impractical as the data distribution maps, i.e., the relationship between joint decision and the resulting distribution shifts, are typically unknown, rendering β unobtainable. To overcome this limitation, we propose a gradient-based sensitivity measure that directly quantifies the impact of decision-induced distribution shifts. Leveraging this measure, we derive convergence guarantees for performatively stable equilibria under a practically feasible assumption of strong monotonicity. Accordingly, we develop a sensitivity-informed repeated retraining algorithm that adjusts players' loss functions based on the sensitivity measure, guaranteeing convergence to performatively stable equilibria for arbitrary data distribution maps. Experiments on prediction error minimization game, Cournot competition, and revenue maximization game show that our approach outperforms state-of-the-art baselines, achieving lower losses and faster convergence.