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.

翻译：博弈论模型与解概念为预测多智能体系统中的集体行为提供了严谨的工具。然而在实践中，不同智能体可能依赖不同的博弈论模型来设计其策略。因此，当这些异构模型相互作用时，实际实现的结果可能显著偏离每个智能体基于其自身局部模型所预期的结果。本文引入博弈与现实差距这一新度量，用于量化多智能体环境中此类模型误设的影响。该差距定义为智能体在多智能体环境（其他智能体可能持有误设模型）中实际获得的效用与其基于自身博弈模型预期效用之间的差值。聚焦于二次型网络博弈，我们证明在（i）外部冲击或（ii）参与者交互网络中的误设都可能导致任意大的博弈与现实差距。我们进一步提出新的网络中心性度量方法，可精确计算二次型网络博弈中的这种差距。分析表明，标准网络中心性度量无法捕捉模型误设的影响，这凸显了需要构建能克服此局限的新结构度量。最后，通过数值实验示例，我们证明现有网络博弈中的中心性度量可能对模型误设的影响产生反直觉的理解。