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THE VALUE OF COMMUNICATION AND COOPERATION WHEN SERVERS ARE STRATEGIC

Part of: Operations research and management science Game theory

Published online by Cambridge University Press:  06 April 2020

M. FACKRELL Open the ORCID record for M. FACKRELL [Opens in a new window] ,
C. LI ,
P. G. TAYLOR Open the ORCID record for P. G. TAYLOR [Opens in a new window]  and
J. WANG Open the ORCID record for J. WANG [Opens in a new window]
M. FACKRELL
Affiliation:
School of Mathematics and Statistics, The University of Melbourne, Victoria3010, Australia email fackrell@unimelb.edu.au, li.c@unimelb.edu.au, taylorpg@unimelb.edu.au, jiesenw@student.unimelb.edu.au
C. LI
Affiliation:
School of Mathematics and Statistics, The University of Melbourne, Victoria3010, Australia email fackrell@unimelb.edu.au, li.c@unimelb.edu.au, taylorpg@unimelb.edu.au, jiesenw@student.unimelb.edu.au
P. G. TAYLOR
Affiliation:
School of Mathematics and Statistics, The University of Melbourne, Victoria3010, Australia email fackrell@unimelb.edu.au, li.c@unimelb.edu.au, taylorpg@unimelb.edu.au, jiesenw@student.unimelb.edu.au
J. WANG*
Affiliation:
School of Mathematics and Statistics, The University of Melbourne, Victoria3010, Australia email fackrell@unimelb.edu.au, li.c@unimelb.edu.au, taylorpg@unimelb.edu.au, jiesenw@student.unimelb.edu.au
*
✉jiesenw@student.unimelb.edu.au
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Abstract

In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In their setup, each server can be either active or inactive and an active server can be requested to transmit a sequence of packets. The servers have varying probabilities of successfully transmitting when they are active, and both servers receive a unit reward if the sequence of packets is transmitted successfully. Guglielmi and Badia provided an analysis of optimal strategies in four scenarios: where each server does not know the other’s successful transmission probability; one of the two servers is always inactive; each server knows the other’s successful transmission probability and they are willing to cooperate.

Unfortunately, the analysis by Guglielmi and Badia contained some errors. In this paper we correct these errors. We discuss three cases where both servers (I) communicate and cooperate; (II) neither communicate nor cooperate; (III) communicate but do not cooperate. In particular, we obtain the unique Nash equilibrium strategy in Case II through a Bayesian game formulation, and demonstrate that there is a region in the parameter space where there are multiple Nash equilibria in Case III. We also quantify the value of communication or cooperation by comparing the social welfare in the three cases, and propose possible regulations to make the Nash equilibrium strategy the socially optimal strategy for both Cases II and III.

Keywords

communicationcooperationtwo-player gameNash equilibriumthreshold policysocial welfareregulation

MSC classification

Primary: 90B50: Management decision making, including multiple objectives
Secondary: 91A05: 2-person games
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 4 , October 2019 , pp. 349 - 367
Copyright
© 2020 Australian Mathematical Society

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Footnotes

*

This is a contribution to the series of invited papers by past ANZIAM medallists (Editorial, Issue 52(1)). P. G. Taylor was awarded the 2019 ANZIAM medal

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