A 2-Layered Game-Theoretic Deep Learning Model for Predicting Lodging Demand: SHAP and Nash Equilibrium

Technical Summary: A 2-Layered Game-Theoretic Deep Learning Model for Predicting Lodging Demand

Problem Statement
Forecasting tourism demand is essential for pricing and revenue management in the hospitality sector. However, the emergence of peer-to-peer platforms like Airbnb has introduced complex, heterogeneous demand patterns that traditional time-series models (e.g., ARIMA, SARIMAX) struggle to capture accurately. Furthermore, advanced machine learning (ML) and deep learning (DL) models, while often more accurate, operate as "black boxes," lacking the interpretability required for stakeholders to trust predictions or understand the drivers of demand. Additionally, existing forecasting models often treat properties in isolation, ignoring the strategic interdependence where hosts adjust pricing and availability based on competitor actions and market dynamics. This study addresses the dual challenges of improving predictive accuracy while enhancing interpretability and incorporating strategic market behavior.

Methodology
The study proposes a hybrid framework integrating deep learning, explainable AI (XAI), and game theory, applied to a dataset of 729,888 daily observations from 1,852 Airbnb listings in Ann Arbor, Michigan (January 2021–December 2022). The methodology operates on two distinct layers:

1. Predictive Modeling and Interpretability (Cooperative Game Layer):

   • Models Tested: The study compares traditional baselines (Linear Regression, SARIMAX) against advanced architectures: Fully Connected Neural Networks (FCNN), Long Short-Term Memory (LSTM), Transformers, and a Transformer–LSTM hybrid.
   • Feature Engineering: 22 features were utilized, including property attributes (bedrooms, capacity), location data (latitude, longitude, zip code), and temporal indicators (holidays, events).
   • SHAP Integration: To address the "black box" issue, Shapley Additive Explanations (SHAP) were applied. Rooted in cooperative game theory, SHAP quantifies the marginal contribution of each feature to the prediction, treating features as "players" contributing to a shared payoff.
   • Scenarios: Three scenarios were tested: (1) using the full feature set, (2) selecting features based on SHAP scores above a threshold, and (3) an expanded selection including top SHAP features plus the next four most significant variables.

2. Strategic Simulation (Competitive Game Layer):

   • Clustering: Data was clustered into four submarkets using K-means clustering based on numerical attributes (price, location, capacity) to ensure competitors within a cluster faced similar demand conditions. The optimal number of clusters ($k=4$) was determined via the elbow method.
   • Game Simulation: Using the best-performing forecasting model (FCNN) to generate demand probabilities, the study simulated 3x3 two-player pricing games (Bertrand and Stackelberg) between pairs of properties within each cluster.
   • Strategies: Players chose between Low, Medium, or High pricing strategies. Payoffs were defined as expected revenue (booking probability $\times$ price). The study analyzed Nash Equilibria (simultaneous moves) and Stackelberg equilibria (sequential moves) to identify stable pricing strategies.

Key Results

• Model Performance: Deep learning models significantly outperformed traditional baselines. In the full feature set (Scenario 1), the FCNN achieved the highest performance (Precision: 92.50%, F1-score: 93.21%, Accuracy: 89.59%, ROC AUC: 95.48%). In Scenario 2 (SHAP-based feature selection), the Transformer model emerged as the top performer (F1-score: 93.11%). The Transformer–LSTM hybrid did not outperform the single best models in any scenario.
• Interpretability: SHAP analysis identified key drivers of demand, including Cleaning Fee, Price, Number of Bathrooms, and geospatial indicators (Latitude, Distance to Stadium). This provided transparent, actionable insights into feature importance.
• Market Dynamics & Equilibria:
  • Cluster 1 (High Price, Low Demand): Both players reached a Nash Equilibrium at "High/High" pricing, suggesting a defensive pricing strategy.
  • Cluster 2 (Low Price, Low Demand): An asymmetric equilibrium emerged where one player maintained high prices while the other competed on the lowest price level, effectively segmenting the market.
  • Cluster 3 (High Demand, Moderate Price): A "Low/High" equilibrium was observed, indicating inelastic demand where properties could sustain high demand regardless of price fluctuations, though strategic interaction suggested complementary pricing roles.
  • Cluster 4 (High Price, High Demand): A "High/High" equilibrium was found, where both players benefited from high pricing bands without triggering adverse consumer reactions.
  • Stackelberg vs. Nash: In all clusters, the Stackelberg (leader-follower) results were identical to the Nash Equilibria, indicating no first-mover advantage in these pairwise markets.

Key Contributions

1. Dual-Layer Game Theory: The study introduces a novel framework applying game theory at two levels: cooperative (SHAP for feature attribution) and competitive (pricing simulation). This moves beyond static forecasting to model strategic interdependencies.
2. Explainable AI Integration: By grounding feature importance in Shapley values, the study bridges the gap between high-accuracy deep learning and the need for theoretical and behavioral interpretability in tourism markets.
3. Dynamic Equilibrium Analysis: Unlike prior studies relying on static assumptions, this research uses ML-generated demand estimates to simulate real-time pricing games, offering a dynamic view of market equilibria.
4. Hybrid Architecture Evaluation: The research provides empirical evidence on the performance of FCNN, LSTM, and Transformer models in the context of short-term rental demand, highlighting the efficacy of FCNN with rich feature sets and Transformers with selective inputs.

Significance and Claims
The paper claims to advance the literature by aligning machine learning interpretability with economic and behavioral reasoning. It posits that treating forecasting features as strategic signals and modeling host interactions through game theory offers a more coherent explanation of market dynamics than accuracy-centered approaches alone.

Practically, the findings suggest that in highly saturated markets, price changes may yield low marginal returns, prompting a shift toward non-price strategies (e.g., listing quality, minimum stays). Conversely, in competitive core markets, specific pricing rules (e.g., matching rival pricing tiers) can be effective. The study concludes that the absence of a first-mover advantage in these pairwise markets implies that hosts should focus on market positioning rather than attempting to set prices first. Finally, the integration of SHAP is presented as a solution to the "black box" barrier, making AI-driven revenue management more transparent and actionable for practitioners.