Historical claims problems

TL;DR

This paper introduces a historical operator for claims problems that incorporates past solutions into current decision-making, extending standard rules to account for historical context in resource claims.

Contribution

It presents a novel operator that extends claims problem rules to include historical information, with a characterization and property preservation analysis.

Findings

The operator effectively incorporates history into claims resolution.

Properties of standard rules are preserved under the operator.

A formal characterization of the operator is provided.

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.