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Simulating Eutopia: Revisiting Long-term Fairness with Outcomes, Performativity, and Dynamics

This paper proposes "Eutopia," a novel simulator that models credit lending as a performative Markov Decision Process to demonstrate that learning with performative dynamics and fairness-aware utilities significantly improves long-term efficiency, equity, and inclusivity compared to traditional approaches that ignore population feedback.

Original authors: Vedant Palit, Udvas Das, Brahim Driss, Debabrota Basu

Published 2026-07-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Vedant Palit, Udvas Das, Brahim Driss, Debabrota Basu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are the captain of a massive, high-tech ship steering through a foggy ocean. This isn't just any ship; it's an AI-driven decision-maker, a digital captain that helps banks decide who gets a loan, who gets a job, or who gets medical care. For a long time, scientists thought of these digital captains as passive observers, like a lighthouse that just shines a beam on the waves without changing them. But in reality, these captains are more like a coach shouting instructions to a team of players. When the coach changes the rules, the players change how they run, how they train, and even who decides to join the game. This "coach effect" is called performativity: the idea that the act of making a prediction changes the very people being predicted on.

Now, imagine the coach is trying to be fair. If they only look at the players' current stats to pick the best team, they might accidentally ignore the players who are talented but haven't had a chance to shine yet. If they keep ignoring them, those players might stop showing up to practice entirely. This creates a vicious cycle where the "fair" decision today makes the team less fair tomorrow. This is the puzzle of long-term fairness: how do we make decisions that are good for everyone right now and keep the whole team strong and equal in the future? It's a tricky dance between making money (efficiency) and making sure no one gets left behind (equity).

This paper, "Simulating Eutopia," dives deep into this dance by building a virtual playground called Eutopia. Think of Eutopia as a super-advanced video game simulator for a bank. In this game, there are two teams of applicants (let's call them the Red Team and the Blue Team), and the AI bank manager has to decide who gets a loan. The twist? The game is "performative." If the AI approves a loan for a Red Team member, that person gets richer, which makes them more likely to apply for another loan next time. If the AI keeps rejecting the Blue Team, they get poorer and eventually stop applying altogether. The AI has to learn not just who is creditworthy now, but how its own choices will change the future of the game.

The researchers used this simulator to test different strategies. They compared "static" strategies (like a robot that follows a fixed rulebook) against "learning" strategies (like a student who learns from mistakes). They also tested different definitions of "fairness." Some strategies cared only about the bank's profit (Utilitarian), some cared about the poorest person getting ahead (Rawlsian), and some tried to balance the bank's profit with the group's wealth (Fairness Lagrangian).

Here is what they found in their simulations:

First, learning matters, but the type of learning matters more. A robot that just looks at today's data and makes a decision (a "one-step predictor") actually made things worse over time. It created a huge gap between the rich and the poor, and the gap kept growing. However, AI agents that learned to think about the long term did much better. Even better, the agents that understood the "performative" nature of the game—meaning they realized their decisions would change the players' future behavior—did the best of all. They managed to keep the wealth gap small and the inequality ratio close to 1 (meaning both teams grew at the same rate) while still making a healthy profit.

Second, how you define fairness changes everything. The paper suggests that there is no single "magic button" for fairness.

If the AI only cares about the bank's profit per group (Decision Maker fairness), the two teams end up with very different wealth levels, even if the bank makes the same amount of money from each. It's like paying two players the same salary but one player has a better coach, so they end up with more skills.
If the AI cares about the actual wealth of the people (Outcome fairness), the results are much more balanced.
The most successful strategy in their simulations was a mix called the Fairness Lagrangian. This approach told the AI: "Maximize total wealth, but if the gap between the Red and Blue teams gets too big, you get a penalty." This strategy allowed the AI to be profitable while keeping the teams relatively equal.

The researchers also discovered a hidden trap. Even when the AI treated the two teams equally on average, the loans often ended up going to the same few wealthy individuals over and over again. This is the "Matthew Effect" (the rich get richer). The simulations showed that while some strategies reduced the gap between the two teams, they sometimes made it harder for new, poorer people to get a loan at all. The most inclusive strategies were those that specifically looked at the "reach rate"—how many unique people got a loan—rather than just the total amount of money lent.

In short, the paper suggests that to build a truly fair future, we can't just use old rules. We need AI that understands that its decisions shape the future. By simulating these complex interactions, the authors found that combining a "learning" approach with a goal that balances profit and social well-being leads to a world where the bank stays in business, and the people stay equal. It's not a solved problem, but the simulation shows a clear path forward: if we teach our digital captains to think about the long game, we might just build a society where everyone gets a fair shot.

Technical Summary: Simulating Eutopia: Revisiting Long-term Fairness with Outcomes, Performativity, and Dynamics

1. Problem Statement

Modern AI-driven Decision Makers (ADMs), such as credit lenders, do not operate in passive environments. Their decisions actively shape the socioeconomic behaviors of the populations they serve, a phenomenon known as performativity. While existing literature on algorithmic fairness has extensively studied short-term metrics (e.g., demographic parity at a single decision point) and long-term fairness in static environments, it largely overlooks two critical realities of modern ADMs:

Endogenous Dynamics: The population's behavior (e.g., application rates, wealth accumulation) changes in response to the ADM's policy.
Outcome vs. Prediction Bias: Most fairness metrics focus on disparities in instantaneous predictions rather than downstream equity (e.g., long-term wealth distribution).

Consequently, learning algorithms optimized for short-term fairness or static long-term fairness may inadvertently amplify structural disadvantages or fail to achieve genuine equity when deployed in performative settings. The paper addresses the question: What are the long-term effects of performative interactions between AI-driven decision makers and human society in terms of both efficiency and equity?

2. Methodology

2.1 Formalization: Performative MDP

The authors formalize the credit lending problem as a Performative Markov Decision Process (PeMDP). Unlike standard MDPs where transition dynamics are exogenous, in a PeMDP, the transition and reward functions are reactive to the deployed policy $\pi$ .

State: Includes applicant features, group membership, group mean wealth, Hawkes intensities (application rates), and cumulative default rates.
Action: Binary lending decisions (approve/deny) for a batch of applicants.
Dynamics:
- Wealth Transition: Approved loans increase borrower wealth if repaid, or result in a loss if defaulted. Denied applicants experience no wealth change.
- Application Dynamics: Modeled via a Hawkes process. The arrival rate of applications for a demographic group is endogenous, responding to observed approval patterns and current group mean wealth (capturing the "Matthew Effect" where wealthier groups apply more frequently).
Objective: The authors adopt an average-reward criterion ( $V^\pi = \lim_{T \to \infty} \frac{1}{T} \mathbb{E}[\sum r_t]$ ) to optimize for steady-state behavior rather than discounted short-term returns.

2.2 Simulation Environment: Eutopia

To address the lack of test-beds for performative fairness, the authors developed Eutopia, a loan simulator.

Key Feature: It is a continual environment where state (wealth, application history) persists across episodes, maintaining the performative feedback loop.
Components:
- Hawkes Arrival Process: Captures temporal clustering of applications driven by group wealth and past approvals.
- Wealth-Transition Model: Simulates wealth accumulation based on loan repayment outcomes.
- Selective Labels: Repayment outcomes are only observed for approved applicants, simulating real-world selection bias.

2.3 Data Generation: LOANLY

To populate Eutopia with realistic data, the authors created LOANLY, a performative data generator.

Base: Built upon the UCI Adult Income dataset to ensure realistic demographic and economic heterogeneity.
Mechanism: Generates initial wealth, ground-truth creditworthiness, and fixed financial types (loan amount, default probability, wealth gain).
Performativity: Encodes parameters that govern how the population responds to decisions over time, allowing the study of how model outputs shape the data used for retraining.

2.4 Learning Algorithms and Objectives

The study compares two learning paradigms:

Passive RL (RL): Standard Policy Gradient (REINFORCE) that treats the environment as static (ignoring distribution shift).
Performative RL (PERL): Performative Policy Gradient (PePG) that explicitly models the dependence of the environment's transition distribution on the policy.

These agents are evaluated across different Fairness Perspectives (Outcome, Decision Maker, Two-Sided) and Utility Functions (Utilitarian, Social Welfare, Rawlsian Max-Min, Fairness Lagrangian).

3. Key Contributions

Eutopia Simulator: The first purpose-built simulator for testing performative fairness in long-term lending, supporting both static (MDP) and performative (PeMDP) modes for direct comparison.
LOANLY Data Generator: A standardized pipeline for generating synthetic lending datasets that encode performative dynamics, enabling the study of how model outputs shape future data without requiring proprietary financial data.
Formal Framework: A formalization of bank lending as an average-reward PeMDP, explicitly modeling the feedback loop between lending decisions, wealth accumulation, and application rates.
Empirical Analysis: A systematic evaluation of how learning models (static vs. performative) and objective designs (fairness-aware vs. utilitarian) influence long-term efficiency and equity.

4. Experimental Results

4.1 Learning with Performative Dynamics Matters

PERL vs. RL: Learning with performative dynamics (PERL) consistently leads to better long-term efficiency and equity compared to passive RL (RL).
Wealth Gaps: PERL achieves lower wealth gaps and inequality ratios than RL across all fairness objectives. For instance, under Rawlsian utility with outcome fairness, PERL reduced the mean wealth gap to 47.2 compared to 49.1 for RL.
Social Welfare: PERL achieves uniformly better social welfare than RL, indicating that modeling the feedback loop is decisive for long-term deployments.

4.2 The Role of Fairness Objectives

Outcome Fairness: Objectives targeting group wealth (Outcome Fairness) generally achieve the best equity-profit balance. Specifically, the Fairness Lagrangian (FL) under outcome fairness yielded the highest profit and social welfare for PERL while maintaining near-parity in inequality ratios ( $\rho \approx 1.01$ ).
No Universal Winner: No single utility function dominates across all metrics (profit, wealth gap, social welfare, inequality ratio). The choice of utility should be treated as a policy decision reflecting regulatory obligations.
Inclusivity: Outcome-based fairness training leads to greater inclusivity. The Fairness Lagrangian under outcome fairness resulted in more equitable distribution of loan access (reach rates) between demographic groups compared to utilitarian profit objectives.

4.3 Micro-level Analysis (Inclusivity and Diversity)

Matthew Effect: Across all configurations, loan concentration within groups increased over time (Lorenz curves moved away from equality).
DM Fairness Limitations: Decision Maker (DM) fairness, which constrains per-step profit disparity, failed to prevent wealth divergence between groups. It resulted in the largest wealth gaps.
Outcome Fairness Trade-offs: While outcome fairness reduced between-group wealth gaps, it sometimes exacerbated within-group concentration (loans concentrated among the already wealthy), particularly under Social Welfare and Fairness Lagrangian objectives.
Reach Rates: Outcome-aware strategies achieved higher reach rates (fraction of unique recipients) than DM fairness, though this came with sharper within-group concentration.

5. Significance and Claims

The paper claims that learning with a proper model of population dynamics (performativity) and well-designed fairness objectives evaluated on social outcomes is essential for ensuring long-term equity.

Beyond Static Fairness: The study demonstrates that static fairness constraints or models that ignore performative shifts are insufficient for long-term equity. Static policies (like one-step predictors) may be immediately profitable but fail to correct the wealth disparities they induce over time.
Design Choices Matter: The choice of learning algorithm (PERL vs. RL) and the fairness objective (e.g., Outcome vs. DM fairness) interact qualitatively. For example, PERL outperforms RL under outcome fairness, but RL can outperform PERL under two-sided fairness.
Policy Implications: The results suggest that achieving long-term equity requires a joint consideration of the learning algorithm's ability to model feedback loops and the specific fairness metrics used to guide optimization. There is no "free lunch"; different objectives prioritize different dimensions of fairness (e.g., between-group equity vs. within-group inclusivity), and these trade-offs must be explicitly managed.

The authors conclude that while their simulator does not mimic the real world perfectly, the non-trivial and difficult-to-anticipate outcomes produced by the performative feedback loops in Eutopia motivate the development of new algorithmic frameworks that acknowledge the multifaceted nature of long-term fairness.