We study a system where many identical customers use a single service.
Each customer experiences both positive externalities (a positive
"network effect") and negative externalities (a "congestion effect")
from other customers using the service. Such a model arises frequently
in practice: application services on wireless networks are a primary
example. We characterize the social optimum, where a social planner
determines the usage level of each customer. We also characterize the
Nash equilibrium achieved when the usage levels are determined by the
customers themselves, in their self-interest. We study the ratio of the
welfare in Nash equilibrium to that in the social optimum. We
demonstrate that there is an *optimal scale*, i.e., a number of
customers at which this ratio is maximized; further, the optimal ratio
is unity. We also show that this same optimal scale maximizes the Nash
welfare of a single individual. We interpret our results in terms of
club formation, and also discuss extensions to a dynamic pricing model
with a single monopolistic service provider.
Bio
Ramesh Johari is an Assistant Professor at Stanford University, with a
full-time appointment in the Department of Management Science and
Engineering, and courtesy appointments in the Departments of Computer
Science and Electrical Engineering. He received an A.B. in Mathematics
from Harvard (1998), a Certificate of Advanced Study in Mathematics from
Cambridge (1999), and a Ph.D. in Electrical Engineering and Computer
Science from MIT (2004). He is also the recipient of First Place in the
INFORMS George E. Nicholson Student Paper Competition (2003), the George
M. Sprowls Award for the best doctoral thesis in computer science at MIT
(2004), honorable mention in the ACM Doctoral Dissertation Award
competition (2005), an Okawa Foundation Research Grant (2005), and an
NSF Career Award (2007). His current research interests include
incentives and pricing in networked systems.