The Value of Communication and Cooperation in a Two-Server Service System

TL;DR

This paper corrects previous analysis of a two-server service system, exploring how communication and cooperation affect optimal strategies, Nash equilibria, and social welfare in different informational and cooperative scenarios.

Contribution

It provides corrected analyses of strategic behaviors, derives Nash equilibria in various cases, and quantifies the impact of communication and cooperation on social welfare.

Findings

Unique Nash equilibrium in non-communicative, non-cooperative case

Multiple Nash equilibria in communication without cooperation case

Communication and cooperation improve social welfare

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 either be 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 in Guglielmi and Badia contained 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.