Game-to-Real Gap: Quantifying the Effect of Model Misspecification in Network Games

2026-01-22

AI Summary

This study addresses the critical issue of model misspecification in heterogeneous multi-agent systems, where inaccuracies—such as unmodeled external shocks or erroneous assumptions about interaction network structure—can cause agents’ realized utilities to deviate substantially from expectations. The paper introduces, for the first time, the concept of the “game-to-real gap” to formally characterize this discrepancy. Building on quadratic network game theory and integrating tools from graph theory and game theory, the authors develop a novel, analytically tractable network centrality measure. Theoretical analysis demonstrates that model misspecification can induce arbitrarily large utility deviations. Numerical experiments validate the efficacy of the proposed centrality metric and further reveal that conventional centrality measures can be highly misleading under model misspecification.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Game-theoretic models and solution concepts provide rigorous tools for predicting collective behavior in multi-agent systems. In practice, however, different agents may rely on different game-theoretic models to design their strategies. As a result, when these heterogeneous models interact, the realized outcome can deviate substantially from the outcome each agent expects based on its own local model. In this work, we introduce the game-to-real gap, a new metric that quantifies the impact of such model misspecification in multi-agent environments. The game-to-real gap is defined as the difference between the utility an agent actually obtains in the multi-agent environment (where other agents may have misspecified models) and the utility it expects under its own game model. Focusing on quadratic network games, we show that misspecifications in either (i) the external shock or (ii) the player interaction network can lead to arbitrarily large game-to-real gaps. We further develop novel network centrality measures that allow exact evaluation of this gap in quadratic network games. Our analysis reveals that standard network centrality measures fail to capture the effects of model misspecification, underscoring the need for new structural metrics that account for this limitation. Finally, through illustrative numerical experiments, we show that existing centrality measures in network games may provide a counterintuitive understanding of the impact of model misspecification.

Problem

• model misspecification
• network games
• game-to-real gap
• multi-agent systems
• utility deviation

Innovation

• game-to-real gap
• model misspecification
• quadratic network games
• network centrality
• multi-agent systems