Dynamic Pareto Optima in Multi-Period Pure-Exchange Economies

2026-03-19

AI Summary

This study investigates Pareto optimal allocations in discrete-time, multi-period pure exchange economies under dynamic risk measures. By introducing the notion of dynamically Pareto optimal allocations, the authors establish a comonotonic improvement theorem and, under distribution-invariant preferences, recursively construct optimal allocations backward from the terminal period using strongly time-consistent dynamic risk measures and comonotonicity arguments. For distortion-based dynamic risk measures, they further derive closed-form solutions. In a two-period setting, the paper explicitly characterizes Pareto optimal allocations that align with agents’ dynamic preferences, thereby demonstrating both the validity and practical tractability of the proposed approach.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

We study a problem of optimal allocation in a discrete-time multi-period pure-exchange economy, where agents have preferences over stochastic endowment processes that are represented by strongly time-consistent dynamic risk measures. We introduce the notion of dynamic Pareto-optimal allocation processes and show that such processes can be constructed recursively starting with the allocation at the terminal time. We further derive a comonotone improvement theorem for allocation processes, and we provide a recursive approach to constructing comonotone dynamic Pareto optima when the agents' preferences are coherent and satisfy a property that we call equidistribution-preserving. In the special case where each agent's dynamic risk measure is of the distortion type, we provide a closed-form characterization of comonotone dynamic Pareto optima. We illustrate our results in a two-period setting.

Problem

• Dynamic Pareto Optima
• Multi-Period Pure-Exchange Economies
• Dynamic Risk Measures
• Optimal Allocation
• Stochastic Endowment Processes

Innovation

• dynamic Pareto optimality
• time-consistent dynamic risk measures
• comonotone improvement
• equidistribution-preserving
• distortion risk measures