AI Plays? {delta}-Rationality Games with Nash Equilibrium as Special Case

2025-06-19

AI Summary

In game theory, a fundamental disconnect exists between behavioral explanations—based on players’ observed payoffs—and normative welfare assessments—based on their true underlying utilities. This impedes coherent analysis when actual behavior deviates systematically from rationality due to cognitive limitations or perception biases. Method: We propose the δ-rational game framework, which explicitly models bounded rationality via a rationality deviation parameter δ and an associated distortion function mapping true utilities to distorted (observed) payoffs. Behavior is rationalized using distorted payoffs, while welfare evaluation remains grounded in true utilities. Contribution/Results: We rigorously prove existence of δ-rational equilibria and show that Nash equilibria emerge as the special case when δ = 0. By unifying payoff distortion under a tunable rationality parameter, our framework bridges descriptive behavioral modeling and prescriptive welfare analysis. It provides a novel paradigm for strategic modeling of AI agents operating under bounded rationality, enabling simultaneous prediction of behavior and evaluation of social welfare.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

A distortion function, which captures the payoff gap between a player's actual payoff and her true payoff, is introduced and used to analyze games. In our proposed framework, we argue that players'actual payoff functions should be used to explain and predict their behaviors, while their true payoff functions should be used to conduct welfare analysis of the outcomes.

Problem

• Analyzing payoff gaps using distortion functions in games
• Explaining player behavior via actual payoff functions
• Conducting welfare analysis with true payoff functions

Innovation

• Introduces distortion function for payoff gap analysis
• Uses actual payoff functions for behavior prediction
• Applies true payoff functions for welfare analysis