Capacity Choice Game in a Multi-Server Queue: Existence of a Nash Equilibrium

24 Pages Posted: 9 Feb 2019 Last revised: 15 Apr 2020

See all articles by Mor Armony

Mor Armony

New York University (NYU) - Department of Information, Operations, and Management Sciences

Guillaume Roels

INSEAD - Technology and Operations Management

Hummy Song

University of Pennsylvania - The Wharton School

Date Written: August 02, 2019

Abstract

In a multi-server, single-queue symmetric capacity choice game, Gopalakrishnan et al. (2016) characterize the existence of a Nash equilibrium under a requirement on the servers’ capacity cost functions, which excludes some highly relevant cases where servers have ample discretion over their choice of service rates. Without that requirement and when servers are free to choose any service rate, potentially leading to an unstable queueing system, the servers’ cost function is ill-behaved and standard tools for establishing the existence of an equilibrium cannot be applied. In this note, we consider a general power capacity cost function in a two-server capacity choice game with no restriction on the servers’ choice of capacity. Relying on a lesser-known result, namely Tarski's intersection theorem, we establish the existence of a Nash equilibrium, thus extending the result by Gopalakrishnan et al. (2016) to our setting. Comparing settings where queue stability is enforceable versus not, we show that there always exists a Nash equilibrium in the former case, unlike in the latter, and that some of the capacity choices that are equilibria in the former case are no longer equilibria in the latter. Our analysis highlights the criticality of the enforceability of system stability on equilibrium outcomes.

Keywords: Queueing Theory, Game Theory, Strategic Servers, Tarski's Intersection Theorem

Suggested Citation

Armony, Mor and Roels, Guillaume and Song, Hummy, Capacity Choice Game in a Multi-Server Queue: Existence of a Nash Equilibrium (August 02, 2019). INSEAD Working Paper No. 2019/33/TOM, NYU Stern School of Business, Available at SSRN: https://ssrn.com/abstract=3321797 or http://dx.doi.org/10.2139/ssrn.3321797

Mor Armony

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States
(212) 998-0291 (Phone)
(212) 995-4227 (Fax)

Guillaume Roels

INSEAD - Technology and Operations Management ( email )

Boulevard de Constance
77 305 Fontainebleau Cedex
France

Hummy Song (Contact Author)

University of Pennsylvania - The Wharton School ( email )

3730 Walnut Street
Philadelphia, PA 19104
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
84
Abstract Views
732
Rank
550,221
PlumX Metrics