Relative entropy and envy-free allocation

null Lonnie Turpin, Jr.; Kelli Bruchhaus; Keith Credo; null Gerard Ornas, Jr.

doi:10.3934/jdg.2022013

Article Contents

2022, Volume 9, Issue 3: 267-282. Doi: 10.3934/jdg.2022013

This issue Previous Article Neighborhood strong superiority and evolutionary stability of polymorphic profiles in asymmetric games Next Article Stress-strength reliability with dependent variables based on copula function

Relative entropy and envy-free allocation

1.
Department of Business Disciplines, McNeese State University, Lake Charles, LA 70607, USA
2.
Department of Management, University of Louisiana at Lafayette, Lafayette, LA 70503, USA
3.
Department of Mathematical Sciences, McNeese State University, Lake Charles, LA 70607, USA

^* Corresponding author: Lonnie Turpin, Jr
^* Corresponding author: Lonnie Turpin, Jr

Received: September 2021

Revised: March 2022

Early access: June 2022

Published: July 2022

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Abstract

In this brief work, we study a basic environment consisting of a single receiver taking actions based on information (called signals) from multiple senders. The receiver is a rational Bayesian who uses optimization as a mechanism to convert the signals to actions. The conversions are gambles as the actions must be taken before signal reception. Formal comparisons of differences between the solution sets of both prior and posterior optimization frameworks and their respective probability distributions are given. The difference in probability distributions (denoted by relative entropy) presents a useful tool for modifying the receiver's level of risk. We then construct a simple scenario where the receiver acts as a proxy in a Shapely-Shubik-style game with two agents focusing on different objectives under a common risk level. Acting on their behalf, an envy-free allocation mechanism is presented to simultaneously satisfy each using the asymmetric assignment model when findings show the objectives require identical actions.

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Mathematics Subject Classification: Primary: 91A05; Secondary: 90C10.

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