pith. sign in

arxiv: 2605.23953 · v1 · pith:AXIG6Z4Unew · submitted 2026-05-11 · 💱 q-fin.TR · cs.GT· cs.LG

Game-Theoretic Modeling of Heterogeneous Investor Interactions for Stock Price Forecasting

Yong Zhang , Xinxiao Wu , Yunde Jia , Che Sun This is my paper

Pith reviewed 2026-06-30 22:35 UTC · model grok-4.3

classification 💱 q-fin.TR cs.GTcs.LG
keywords stock price forecastinggame-theoretic modelingheterogeneous graphsinvestor interactionsgraph networksfinancial time series
0
0 comments X

The pith

Embedding game theory into heterogeneous graphs models investor interactions to forecast stock prices.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to show that stock price forecasting improves when investor behaviors are treated as dynamic strategic games embedded directly in a heterogeneous graph of stocks and participants. Prior methods rely on fixed assumptions about time patterns within single stocks or predefined links across stocks, leaving the actual drivers of price changes unmodeled. By placing game mechanisms inside the graph and adding time-based encodings, the structure lets nodes update in response to shifting interactions, producing forecasts that reflect ongoing market plays. If the approach holds, forecasts would move from static snapshots to representations that track how different investor types adjust strategies over successive periods.

Core claim

The authors claim that embedding game-theoretic mechanisms into the heterogeneous graph structure finely models the dynamic strategic interactions among heterogeneous investors with respect to target stocks. Temporal positional encoding is used to reflect the differentiated influences of each game event at different time steps, while heterogeneous graph networks proxy the intricate dynamics of the stock market through these investor games and enable real-time information propagation and node updates among all nodes, leading to outperformance over state-of-the-art methods on two benchmark datasets.

What carries the argument

Embedding game-theoretic mechanisms into the heterogeneous graph structure to model dynamic strategic interactions among heterogeneous investors.

If this is right

  • Dynamic investor games allow the model to adapt forecasts as interactions change within the time window.
  • Temporal positional encoding lets each game event exert a distinct effect on future prices based on its timing.
  • Real-time propagation through the heterogeneous graph updates all investor and stock nodes together.
  • The resulting forecasts outperform existing methods that use only static temporal or spatial dependencies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same graph-game structure could be tested on related tasks such as volatility prediction by redefining the payoff rules.
  • High-frequency trading records could serve as a direct check on whether the modeled interactions match observed order flows.
  • Different investor categories might be calibrated against public holdings data to see if the heterogeneity assumption improves accuracy further.

Load-bearing premise

That the complex market dynamics driving stock prices can be represented as strategic games among different investor types inside a graph network.

What would settle it

A new dataset in which the full model produces higher forecasting error than standard time-series or graph methods that omit the game-theoretic component.

Figures

Figures reproduced from arXiv: 2605.23953 by Che Sun, Xinxiao Wu, Yong Zhang, Yunde Jia.

Figure 1
Figure 1. Figure 1: Overview of our GameStock architecture. as G = (V, E, A, R), where each node v ∈ V is associated with a node type ϕ(v) ∈ A, and each heterogeneous edge e ∈ E corresponds to a relation type ψ(e) ∈ R. Game Theory In our framework, all investors in the stock market are categorized into three types, namely institutions, hot money, and retail investors. The strategic and capital games surrounding the target sto… view at source ↗
read the original abstract

Accurate stock price forecasting has consistently remained a pivotal yet challenging FinTech task that underpins quantitative trading and investment decision making. Recent efforts have been dedicated to modeling various complex relationships among stocks in the stock market toward more reliable stock price forecasting.These methods depend heavily on strong static prior assumptions by modeling either temporal dependencies within individual stocks or spatial dependencies across different stocks based on predefined structures, while the complex market dynamics that drive stock price movements remain unexplored. To alleviate this issue, we propose a novel game-theoretic modeling method that captures heterogeneous investor interactions for stock price forecasting. The core idea is to embed game-theoretic mechanisms into the heterogeneous graph structure to finely model the dynamic strategic interactions among heterogeneous investors with respect to target stocks. Additionally, temporal positional encoding is adopted to reflect the differentiated influences of each game event at different time steps within the time window on future stock price movements. Leveraging heterogeneous graph networks, we proxy the intricate dynamics of the stock market through investor games and enable real-time information propagation and node updates among all nodes. Extensive experiments conducted on two real-world benchmark dataset demonstrate that our method effectively outperforms state-of-the-art stock price forecasting methods.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper claims to introduce a novel game-theoretic modeling method that embeds game-theoretic mechanisms into heterogeneous graph structures to capture dynamic strategic interactions among heterogeneous investors for stock price forecasting. Temporal positional encoding is used to account for time-differentiated game events, and heterogeneous graph networks enable information propagation; the approach is reported to outperform state-of-the-art methods on two real-world benchmark datasets.

Significance. If the central claim holds with rigorous validation, the work could advance financial forecasting by incorporating strategic investor behavior into graph-based models, moving beyond static temporal or relational assumptions. Strengths such as the explicit use of game-theoretic payoffs and temporal encoding would be notable if accompanied by reproducible code or parameter-free derivations, but these are not evident from the provided description.

major comments (3)
  1. [Abstract] Abstract: the assertion of outperformance on two benchmark datasets supplies no experimental details, baselines, statistical tests, or error analysis. Stock-price claims are especially vulnerable to overfitting and post-hoc tuning; this absence is load-bearing for evaluating the central claim.
  2. [Abstract] Abstract (core idea): the premise that embedding game-theoretic mechanisms into the heterogeneous graph 'finely model[s] the dynamic strategic interactions among heterogeneous investors' is not supported by an explicit construction. Standard benchmarks contain only price/volume series and static stock relations with no per-investor actions, order books, or identities; without a described proxy (e.g., inferred investor nodes or payoff matrices derived from observed trades), the game-theoretic label risks being nominal.
  3. [Method (inferred from abstract description)] The manuscript provides no indication of how game payoff parameters or equilibrium computations are obtained or approximated inside the forward pass, which directly affects whether the model separates from conventional heterogeneous graph neural networks.
minor comments (2)
  1. [Abstract] The abstract refers to 'two real-world benchmark dataset' (singular/plural inconsistency) without naming the datasets or providing references.
  2. Clarify the precise meaning of 'heterogeneous investors' versus the heterogeneous graph structure to avoid terminological overlap.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight important areas where additional clarity is needed, particularly regarding experimental details and the explicit technical construction of the game-theoretic components. We address each point below and commit to revisions that strengthen the presentation without altering the core contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion of outperformance on two benchmark datasets supplies no experimental details, baselines, statistical tests, or error analysis. Stock-price claims are especially vulnerable to overfitting and post-hoc tuning; this absence is load-bearing for evaluating the central claim.

    Authors: We agree that the abstract, being concise by nature, omits key experimental specifics that would better support the outperformance claim. The full manuscript contains a dedicated experiments section (Section 4) reporting results on two benchmark datasets with comparisons to multiple state-of-the-art baselines, including performance metrics, and some robustness checks. However, to directly address the concern, we will revise the abstract to include brief mentions of the datasets, primary baselines, and statistical significance of improvements. We will also ensure the experiments section explicitly discusses error analysis and steps taken to mitigate overfitting risks such as cross-validation and hyperparameter sensitivity tests. revision: yes

  2. Referee: [Abstract] Abstract (core idea): the premise that embedding game-theoretic mechanisms into the heterogeneous graph 'finely model[s] the dynamic strategic interactions among heterogeneous investors' is not supported by an explicit construction. Standard benchmarks contain only price/volume series and static stock relations with no per-investor actions, order books, or identities; without a described proxy (e.g., inferred investor nodes or payoff matrices derived from observed trades), the game-theoretic label risks being nominal.

    Authors: This is a fair observation based on the abstract's high-level description. The method section constructs the heterogeneous graph by treating different investor categories (e.g., derived from trading volume and frequency patterns in the price/volume data) as distinct node types, with edges representing inferred interactions. Game payoffs are defined using observed price movements as utility signals for each investor type relative to target stocks. To eliminate any ambiguity and make the proxy explicit, we will add a new subsection detailing the node-type inference process, the payoff matrix formulation from aggregate data, and how this differs from purely relational graph models. revision: yes

  3. Referee: [Method (inferred from abstract description)] The manuscript provides no indication of how game payoff parameters or equilibrium computations are obtained or approximated inside the forward pass, which directly affects whether the model separates from conventional heterogeneous graph neural networks.

    Authors: We acknowledge that the abstract does not convey the implementation details. The method integrates a differentiable approximation of Nash equilibrium within the heterogeneous graph propagation step, where payoff parameters are learned end-to-end as part of the network weights, combined with the temporal positional encoding. This is intended to differentiate the approach from standard HGNNs by explicitly incorporating strategic update rules. To clarify this distinction and enable reproducibility, we will expand the method section with pseudocode for the forward pass, explicit formulas for the equilibrium approximation, and ablation studies isolating the game-theoretic component. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model proposal evaluated empirically on external benchmarks.

full rationale

The provided abstract and description contain no equations, derivation steps, or self-citations that reduce the central claim to its inputs by construction. The paper proposes embedding game-theoretic mechanisms into a heterogeneous graph and reports outperformance on two real-world benchmark datasets via standard training/evaluation. This is an empirical modeling claim against external data, not a self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation chain. No load-bearing step is shown that equates the 'game-theoretic' label or forecasting result to the input data by definition. Per the rules, self-contained evaluation on benchmarks receives score 0-2.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Review performed on abstract only; full model specification, loss functions, and training details unavailable. Free parameters and axioms listed are inferred at the highest level from the abstract description.

free parameters (1)
  • graph neural network weights and game payoff parameters
    All neural network and game-theoretic parameters are fitted to the benchmark stock datasets to achieve the reported forecasting performance.
axioms (2)
  • domain assumption Investor interactions with respect to target stocks can be represented as strategic games inside a heterogeneous graph
    This is the core modeling choice stated in the abstract.
  • domain assumption Temporal positional encoding can differentiate the influence of game events at different time steps
    Invoked to handle time-window effects on future prices.

pith-pipeline@v0.9.1-grok · 5735 in / 1409 out tokens · 30529 ms · 2026-06-30T22:35:33.918383+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

10 extracted references · 7 canonical work pages · 3 internal anchors

  1. [1]

    Comparison of arima and artificial neural networks models for stock price prediction.Journal of Applied Mathematics, 2014(1):614342,

    Ayodele Ariyo Adebiyi, Aderemi Oluyinka Adewumi, and Charles Korede Ayo. Comparison of arima and artificial neural networks models for stock price prediction.Journal of Applied Mathematics, 2014(1):614342,

    2014

  2. [2]

    Enhancing Stock Movement Prediction with Adversarial Training

    Fuli Feng, Huimin Chen, Xiangnan He, Ji Ding, Maosong Sun, and Tat-Seng Chua. Enhancing stock movement prediction with adversarial training.arXiv preprint arXiv:1810.09936,

    work page internal anchor Pith review Pith/arXiv arXiv

  3. [3]

    Predicting the direction of stock market prices using random forest

    Luckyson Khaidem, Snehanshu Saha, and Sudeepa Roy Dey. Predicting the direction of stock market prices using random forest.arXiv preprint arXiv:1605.00003,

    work page internal anchor Pith review Pith/arXiv arXiv

  4. [4]

    Hats: A hierarchical graph attention network for stock movement prediction.arXiv preprint arXiv:1908.07999,

    Raehyun Kim, Chan Ho So, Minbyul Jeong, Sanghoon Lee, Jinkyu Kim, and Jaewoo Kang. Hats: A hierarchical graph attention network for stock movement prediction.arXiv preprint arXiv:1908.07999,

    work page arXiv 1908

  5. [5]

    Mera: Mixture of experts with retrieval-augmented representation for modeling diversified stock patterns

    YuJun Liu, Chen-Hui Song, Peiyuan Liu, Naiqi Li, Tao Dai, Jigang Bao, Yong Jiang, and Shu-Tao Xia. Mera: Mixture of experts with retrieval-augmented representation for modeling diversified stock patterns. InCompanion Proceedings of the ACM on Web Conference 2025, pages 1148–1152,

    2025

  6. [6]

    Strategic behavior of large language models: Game structure vs

    Nunzio Lorè and Babak Heydari. Strategic behavior of large language models: Game structure vs. contextual framing.arXiv preprint arXiv:2309.05898,

    work page arXiv

  7. [7]

    A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction

    Yao Qin, Dongjin Song, Haifeng Chen, Wei Cheng, Guofei Jiang, and Garrison Cottrell. A dual-stage attention-based recurrent neural network for time series prediction.arXiv preprint arXiv:1704.02971,

    work page internal anchor Pith review Pith/arXiv arXiv

  8. [8]

    Simulating human strategic behavior: Comparing single and multi-agent llms.arXiv preprint arXiv:2402.08189,

    12 Karthik Sreedhar and Lydia Chilton. Simulating human strategic behavior: Comparing single and multi-agent llms.arXiv preprint arXiv:2402.08189,

    work page arXiv

  9. [9]

    Alphastock: A buying-winners- and-selling-losers investment strategy using interpretable deep reinforcement attention networks

    Jingyuan Wang, Yang Zhang, Ke Tang, Junjie Wu, and Zhang Xiong. Alphastock: A buying-winners- and-selling-losers investment strategy using interpretable deep reinforcement attention networks. InProceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining, pages 1900–1908,

    1900

  10. [10]

    Relation-aware transformer for portfolio policy learning

    Ke Xu, Yifan Zhang, Deheng Ye, Peilin Zhao, and Mingkui Tan. Relation-aware transformer for portfolio policy learning. InProceedings of the twenty-ninth international conference on international joint conferences on artificial intelligence, pages 4647–4653, 2021a. Wentao Xu, Weiqing Liu, Lewen Wang, Yingce Xia, Jiang Bian, Jian Yin, and Tie-Yan Liu. Hist:...

    work page arXiv 2015