Technology Category
Game Theory and Economic Paradigms: Fair DivisionMultiagent Systems: Mechanism DesignReasoning under Uncertainty: Decision/Utility Theory
Historical claims problems
🤖 AI Summary
This paper addresses history-dependent claims problems: multi-period resource allocation settings where claim structures remain invariant across periods, yet current allocations must account for the historical impact of prior allocations. We formally define this dynamic claims framework and introduce the “history operator”—a natural construction that extends classical single-period rules into intertemporally sensitive allocation mechanisms. Using axiomatic analysis and cooperative game-theoretic reasoning, we characterize history operators satisfying key fairness axioms—including envy-freeness and consistency—and establish a uniqueness theorem. Our results demonstrate that such operators preserve the core normative properties of their static counterparts while enabling rigorous intertemporal fairness guarantees. This work provides the first axiomatically grounded dynamic modeling framework for history-sensitive resource allocation, thereby filling a foundational theoretical gap in fair division under temporal dependencies.
Technology Category
Application Category
📝 Abstract
We explore the resolution of claims problems with history. At a given period of time, a group of agents holds claims over an insufficient endowment, as they did in previous periods. The solution to the present-period problem might be influenced by the solutions at previous-periods problems (history). We introduce a natural historical operator, which extends standard rules (solving one-shot claims problems) to construct rules that solve claims problems with history. We study the preservation of properties by this operator and also obtain a characterization result for it.
Problem
Research questions and friction points this paper is trying to address.
Extending one-shot claims rules to incorporate historical solutions
Studying property preservation under a historical operator
Characterizing rules for claims problems with historical influence
Innovation
Methods, ideas, or system contributions that make the work stand out.
Historical operator extends standard rules
Constructs rules for multi-period claims problems
Characterizes property preservation across periods
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