Title: Evolutionary Prediction Games
Venue: NeurIPS 2025
Accepted: yes
Keywords: Evolutionary Game Theory

Feedback Loops

Stateful Performative Prediction

Potential Games

Replicator Dynamics
Abstract: When a prediction algorithm serves a collection of users, disparities in prediction quality are likely to emerge. If users respond to accurate predictions by increasing engagement, inviting friends, or adopting trends, repeated learning creates a feedback loop that shapes both the model and the population of its users. In this work, we introduce evolutionary prediction games, a framework grounded in evolutionary game theory which models such feedback loops as natural-selection processes among groups of users. Our theoretical analysis reveals a gap between idealized and real-world learning settings: In idealized settings with unlimited data and computational power, repeated learning creates competition and promotes competitive exclusion across a broad class of behavioral dynamics. However, under realistic constraints such as finite data, limited compute, or risk of overfitting, we show that stable coexistence and mutualistic symbiosis between groups becomes possible. We analyze these possibilities in terms of their stability and feasibility, present mechanisms that can sustain their existence, and empirically demonstrate our findings.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces evolutionary predictive games, which are a class of evolutionary games in which a classifier and the underlying data distribution co-evolve in a feedback loop with dynamics driven by payoffs defined by average prediction performance. Analysis is carried out to show that, under perfect learning (optimization) and perfect computation of population-level expectations, the evolutionary predictive games monotonically increase in the classifier's accuracy and converge to Nash equilibria with singleton support (meaning only one group of the data distribution remains at play). It is shown that various alternative problem setups can give rise to co-existence of multiple groups at (stable) Nash equilibrium, e.g., by using surrogate loss functions or different learning algorithms. Experiments on MNIST and CIFAR-10 are conducted to empirically corroborate the theory.\n\nSTRENGTHS AND WEAKNESSES:\nQuality: After carefully reviewing the theoretical developments of the paper, the submission appears to be rigorous and technically sound. The key claim (namely, that an analysis is provided for the proposed evolutionary prediction games showing that they exhibit competitive exclusion in the idealized setting of unlimited knowledge of the data distribution, and that stable co-existence can arise in the setting of finite data) is supported through the theoretical developments, and corroborated by the experiments. The theoretical and experimental methods used are appropriate for the problem at hand, and the manuscript culminates into a nice, \"complete\" work. The authors do not explicitly discuss weaknesses or limitations of their work (see my \"Questions\" #6 and #8 for specific instances where this could be improved), but they do briefly mention avenues for future work and related discussion in the conclusion of the paper.\n\nClarity: For the most part, the submission is well-written and well-organized. I have enumerated a few small suggestions for improvement to the writing and presentation in the \"Questions\" below. Enough details of the theoretical proofs and experimental setup are provided (in the supplemental materials) to reproduce the results. The primary weakness in the paper's clarity is that the introduction is quite sparse in terms of the number of references, making it potentially difficult for a reader to jump to relevant work that is prerequisite in fully understanding and appreciating the work at hand. See my \"Question\" #1 below for more details.\n\nSignificance: I find the theoretical findings of competitive exclusion in the ideal setting and stable co-existence in other, non-ideal settings, to be significant to those interested in the intersection of evolutionary game theory and ML. The results are likely not very significant to ML as a whole, which is okay. I suspect that other researchers are likely to build upon the theoretical framework and ideas proposed here. The submission does not necessarily address tasks in better ways than previous works, but rather it provides a novel theoretical framework that, to the best of my knowledge, is unique to the community. The theory developed indeed advances our understanding of the proposed evolutionary prediction games, as the conclusions are not immediately or intuitively obvious.\n\nOriginality: Not only does the work introduce a novel problem setup at the interesting intersection of evolutionary game theory and machine learning, but it provides novel theoretical insights about the problem. The authors could better clarify how their work differs from previous contributions by providing more citations throughout the motivations, problem setup, and introduction of the paper (see my \"Question\" #1 below).\n\nQUESTIONS:\n1. The introduction is very sparse in terms of references. It would be good to support your motivating assertions with citations. For example: \"However, while generally beneficial, promoting accuracy blindly can have unexpected, and in some cases undesired, consequences.\" Can you give references that demonstrate such undesired consequences? For instance, there is a body of influential work that studies accuracy-robustness tradeoffs in ML models that you may want to mention and cite. There are currently no references in the first four paragraphs.\n2. Another important example of where there really should be some specific references cited is the list given in the sentence \"Such dynamics arise across domains:...\"\n3. ‘compete’ Here, you are using single quotes, but before, you used double quotes. It would be good to maintain consistency in your notations and writing style.\n4. Figure 1 is not introduced or discussed at all in the main text of the paper. It would be good to do this, to indicate to the reader when is a natural time to go and look at Figure 1.\n5. Proposition 1: The \"overall accuracy equality fairness criterion in expectation\" property is referred to in Proposition 1, but its definition is deferred to the Appendix. It is fine to defer the proof of Proposition 1 to the Appendix, but it is preferable to include all definitions used in the main text, in the main text, for self-containedness reasons.\n6. \"Overall Accuracy Equality Fairness\": The way you have defined this criterion doesn't quite seem to fully capture \"fairness\" to me. Specifically, how can you say that you achieve fairness if the equality in prediction accuracy only holds for groups that remain at play in Nash equilibrium, unless the Nash equilibrium has full support? For example, if the dynamics converge to a Nash equilibrium with a single index of support, meaning all but one group have effectively been driven out of the game, then how is that fair for the groups that have been driven out?\n7. \"fixed points of the dynamical system coincide with the Nash equilibria\" You may want to mention that this is a property known as \"Nash stationarity.\"\n8. It seems a little misleading in the paragraph of line 169 to claim that all of your three assumptions are satisfied by the dynamics described in Section 1 and Appendix C, and to throw in the \"exception\" that imitative dynamics don't satisfy Nash stationarity into the footnote 1, and to not mention in the main text that the replicator dynamics are imitative dynamics. That is, the replicator dynamics that you seem to focus on do not satisfy your assumption of Nash stationarity, but the reader would need to piece this together themselves by carefully reading footnote 1 and identifying that replicator dynamics are imitative (which you don't explicitly define or mention). If your main theoretical results hold for dynamics that have unstable non-Nash stationary points, then why bother making the Nash stationarity assumption at all?\n9. Line 197: There are two periods in the sentence with footnote 2.\n10. Line 298 typo: \"dynamcis\"\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-28"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nUnder the framework of evolutionary game theory, this paper provides evolutionary prediction games to study the interplay between the accuracy of prediction algorithms and user retention rates. Moreover, a theoretical analysis is provided to investigate the equilibria of the games. This is interesting. However, some details of the evolutionary prediction games should be clarified, like how does a user change the group. In addition, from the perspective of improving the performance of prediction algorithms, this paper lacks a relevant study and explanation.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**  \nThis paper originally presents evolutionary prediction games to study the feedback loop between the accuracy of prediction algorithms and user behavior. This provides a new perspective for prediction algorithms.\n\n**Weaknesses**  \n1. The introduction is not easy to follow. The accuracy of sentences should be further improved. For example, in line 19, what kinds of decision-making are included in personalized education? In line 23, what does social outcome mean here? I think the experiments do not focus on any data from real platforms. In line 25, \"But in social settings, ...\", I think this is not about social settings. For any platforms, which collect data from users to train their prediction algorithms, they may exhibit the feedback loop between users and the accuracy of prediction algorithms. In line 35, \"Common to ...\", What does group structure mean here? What does the relation between prediction algorithm and group?\n2. Why do you divide the population into $K$ groups? Is it necessary for the evolutionary prediction games?\n3. In line 104, the group-specific distribution $D_k$ is assumed to be fixed. Meanwhile, users are able to decide to leave a group and reshape the population composition $p$. Thus, once a user leaves the group $k$, the distribution $D_k$ changes. This seems to contradict the assumption.\n4. In lines 111-113, can you give more details about how users change their groups? For example, under what conditions will a user leave their current group? How does a user choose which new group to join?\n4. In line 211, how can you ensure the existence of $A^{opt}$? What are the conditions for the existence of $A^{opt}$?\n6. Theorem 2 states the existence of such an evolutionary prediction game. What are the conditions for the existence? \n7. This paper studies the co-evolutionary dynamics between prediction algorithms and user behavior. Based on the stable states of the dynamics, can you give some insights into the design of prediction algorithms? \n8. In experiments, can you give a comparison between different prediction algorithms?\n\nQUESTIONS:\nPlease see the weaknesses above.\n\nLIMITATIONS:\nBased on the study of the co-evolutionary dynamics between the prediction algorithms and user behavior, can the authors give some insights into the design of prediction algorithms?", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper instantiates a model of a population of user participation decisions in a prediction system. The population is broken into types. If predictions about a type are good, more individuals of that type will join the system. If predictions about a type are less good, fewer individuals will participate. The system at a given point in time is described by the type-makeup of the population and different population distributions may yield different predictors (optimized for accuracy). This describes situations like content recommendation systems where user participation decisions and prediction quality may generate positive feedback loops. The model is instantiated as an evolutionary game. The main results in the paper are theoretical. They include:\n- Thm 1: If the accuracy of the predictor is uniform over a hypothesis class, accuracy improves, there exists a stable (attracting neighboring states) equilibrium, one type makes up the whole population in any stable equilibrium, and there may be unstable equilibria with more than two types.\n- Thm 2: If the predictor is optimized by a proxy loss, there exists a equilibrium with multiple types that is stable. The intuition is that the proxy induces\n- Prop 2: If the data used to train the predictive system can be reweighted, unstable equilibria can be made stable.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n- The analysis seems correct.\n- The area of prediction under dynamics or performativity is interesting and under-explored.\n\nWeaknesses:\n\n- Real platforms seem to have a diversity of users, it seems like the results in the paper are discordant with real, e.g., recommendation systems. What explains this? Is it that the evolution dynamics are not as powerful in real life? Is it explained by the proxy objectives that platforms must use? Are the platforms training on a diversity of data? Are platforms not in equilibrium? I would have liked more grappling with the implications of these results for platform practices or how we understand them.\n- Generally, I did not think the theoretical take-aways were very surprising. Theorem 2 in particular seems weak since it is an existence proof that relaxing optimality of the objective can yield stable multi-group equilibria.\n- I did not feel the related work on evolutionary prediction games was sufficiently detailed. Results in this paper seem like they might be special cases of general analyses of population games. (Intuitively, it seems like the conclusion of Thm 1 should hold quite generally and any setting where growth begets growth should yield these kinds of conclusions.) On the other hand, I am not familiar enough with population games to verify whether this kind of claim is proved elsewhere. The related work says “competitive exclusion” is well-studied, which suggests to me there should be related results.\n- I did not find the experiments particularly informative. It would be nice to highlight qualitative take-aways or more nuances rather than just reporting the type breakdown in the equilibria.\n\nQUESTIONS:\nWhat does it mean to be fitness maximizing? I don’t see where it was defined. Is it the maximum (over p) fitness summed over types?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces an interesting framework that the authors name evolutionary prediction games. The motivation is that distributions of trianing data are composed of users who choose to use the platform, which can often depend on the quality of predictions. Thus there is a feedback loop where the prediction model can shape the population of users and the population of users will impact the distribution of data the model continues to be trained on. The authors analyze this setting use a population game, coming from evolutionary game theory. Their Theorem 1 shows that repeatedly training with new data will lead to dominance of the groups that had highest fitness to begin with, essentially allowing them to dominate the platform. Their second theorem provides conditions, however, under which there can be coexistence. Furthermore, the authors provide experimental results on MNIST and CIFAR-10 demonstrating the theoretical results.\n\nSTRENGTHS AND WEAKNESSES:\nThe framing of evolutionary prediction games is really interesting and addresses a real issue faced by platforms that heavily rely on their prediction algorithms for user-retention (eg. TikTok). I really like it. The theorem are the natural type of result a reader would wish to see upon introduction of a new setting such as this, and the technical details are very well explicated in the main text and proven in the supplementary material. The technical results are relevant to the introduced setting but non trivial. Clear proof sketches and helpful interpretations are given for the main two theorems. Additionally, the figures are very clear and helpful. The experiments are simple but illustrative. \n\nThe main weakness that stands out to me is that the experimental results while illustrative of the theoretical results, don't immediately appear to be very representative of the main motivations for this framework in practice. Although it would of course be difficult to obtain a platform's worth of such data, an experiment more closely mimicking such settings would be very compelling.\n\nQUESTIONS:\nAlthough there is discussion in the supplement around related work, I wonder if it would be possible to highlight more in terms of what the author's believe evolutionary potential games will allow us to achieve in terms of gains in production ML systems compared to previous literature?\n\nAlluding to the weakness mentioned above, I wonder if there is any setting perhaps from a fairness benchmark dataset that would be closer to the motivations of the paper?\n\nGiven the results in Theorem 1 and Theorem 2, is there a situation in which the system could first evolve into domination by one group but by retraining grow to the mixed setting with multiple groups besides just changing to assumptions of Theorem 2?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-03"}