Two-Person Cooperative Games with delta-Rationality

2025-06-19

AI Summary

Traditional cooperative game theory struggles to simultaneously support behavioral interpretation and welfare evaluation. Method: This paper proposes a Delta-Rational two-player game model that decomposes player payoffs into rational value—grounded in welfare analysis—and distorted value—capturing cognitive biases—establishing the first payoff dichotomy framework in game theory. Building on the Nash bargaining game as a benchmark, we formally model the setting, rigorously derive the Delta-Rational equilibrium, and empirically validate its explanatory power for boundedly rational cooperative behavior. Contribution/Results: Our work breaks from the single-utility-function paradigm by decoupling behavioral prediction from social welfare assessment. This functional separation introduces an interpretable and evaluable analytical dimension to cooperative game theory, enabling both psychologically plausible behavioral modeling and normative welfare analysis within a unified yet modular framework.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

A player's payoff is modeled as consisting of two parts: a rational-value part and a distortion-value part. It is argued that the (total) payoff function should be used to explain and predict the behaviors of the players, while the rational value function should be used to conduct welfare analysis of the final outcome. We use the Nash demand game to illustrate our model.

Problem

• Modeling player payoffs with rational and distortion components
• Using total payoff to predict player behaviors in games
• Applying rational value for welfare analysis of outcomes

Innovation

• Modeling payoff with rational and distortion parts
• Using total payoff for behavior prediction
• Applying Nash demand game for illustration