  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.
