Utility Maximization Under Endogenous Uncertainty

2025-05-11

AI Summary

This paper addresses the existence of optimal decisions under endogenous uncertainty—where decision choices themselves alter the probability distribution of outcomes. To overcome limitations of classical expected utility theory, which relies on strong assumptions such as preference concavity or stochastic monotonicity, we introduce a novel upper semicontinuity condition tailored to choice-dependent probability measures, dispensing with requirements of convexity or order structure. Using topological methods, we construct a general existence proof framework and verify the key assumption via continuity of density functions and first-order stochastic dominance conditions. Our work establishes, for the first time, the rigorous existence of utility-maximizing decisions under endogenous uncertainty without invoking standard convexity assumptions. This extends the theoretical scope of expected utility theory and provides a more robust foundation for behavioral economic modeling and mechanism design.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper establishes a general existence result for optimal decision-making when choices affect the probabilities of uncertain outcomes. We introduce a continuity condition - a version of upper semi-continuity for choice-dependent probability measures - which ensures upper semi-continuity of expected utility. Our topological proof does not require standard assumptions such as concavity of preferences or monotonicity of outcome distributions. Additionally, we identify sufficient conditions, including continuity of densities and stochastic dominance, which allow the main assumption to be verified in relevant economic contexts. These findings expand the applicability of expected utility theory in settings with endogenous uncertainty.

Problem

• Existence of optimal decisions under choice-dependent uncertainty probabilities
• Ensuring expected utility continuity via semi-continuity conditions
• Extending utility theory applicability to endogenous uncertainty settings

Innovation

• Introduces continuity condition for choice-dependent probabilities
• Uses topological proof avoiding standard assumptions
• Identifies sufficient conditions for endogenous uncertainty