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SUMMARY:Positive Externalities\, Negative Externalities\, and Optimal Scal
 e - Ramesh Johari\,  Stanford University
DTSTART:20071114T140000Z
DTEND:20071114T150000Z
UID:TALK8392@talks.cam.ac.uk
CONTACT:5698
DESCRIPTION:We study a system where many identical customers use a single 
 service.\nEach customer experiences both positive externalities (a positiv
 e\n"network effect") and negative externalities (a "congestion effect")\nf
 rom other customers using the service. Such a model arises frequently\nin 
 practice: application services on wireless networks\, peer-to-peer\nnetwor
 ks\, and social networks are examples.  We characterize the social\noptimu
 m\, where a social planner determines the usage level of each\ncustomer. W
 e also characterize the Nash equilibrium achieved when the\nusage levels a
 re determined by the customers themselves\, in their\nself-interest. We st
 udy the ratio of the welfare in Nash equilibrium to\nthat in the social op
 timum. We demonstrate that there is an *optimal\nscale*\, i.e.\, a number 
 of customers at which this ratio is maximized\;\nfurther\, the optimal rat
 io is unity. We also show that this same optimal\nscale maximizes the Nash
  welfare of a single individual. We interpret\nour results in terms of clu
 b formation\, and study the size of the club\nas the impact of the positiv
 e externality grows.\n\nJoint work with Sunil Kumar\, Stanford GSB.\n
LOCATION: Centre for Mathematical Sciences\, Room 12
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