Network game with a probabilistic description of user types

This paper presents a hierarchical network game of ISPs and users, and introduces three classes of network games based on information structure: complete information, partially incomplete information, and totally incomplete information. Following the approach developed by Basar and Srikant (2002), the existence and uniqueness of the Nash equilibrium is established for the users´ game under complete information (and thus also under partially incomplete information). Furthermore, a sufficient condition for the existence of a unique and stable pure strategy Bayesian equilibrium is obtained for a special two user case under totally incomplete information. The multiple user case with quadratic utility functions is also investigated. Our analysis concludes that incomplete information is a disadvantage for the ISP and the less aggressive users, but is advantageous for the more aggressive users. Also, numerical results indicate that whether the ISP benefits or not from partially incomplete information (users sharing information) compared with totally incomplete information is determined by the number of users.