### On the existence of equilibria in noncooperative optimal flow controlOn the existence of equilibria in noncooperative optimal flow control

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 Author Korilis, Yannis A. ♦ Lazar, Aurel A. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1995 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Nash equilibria ♦ Fixed points ♦ Flow control ♦ Game theory Abstract The existence of Nash equilibria in noncooperative flow control in a general product-form network shared by $\textit{K}$ users is investigated. The performance objective of each user is to maximize its average throughput subject to an upper bound on its average time-delay. Previous attempts to study existence of equilibria for this flow control model were not successful, partly because the time-delay constraints couple the strategy spaces of the individual users in a way that does not allow the application of standard equilibrium existence theorems from the game theory literature. To overcome this difficulty, a more general approach to study the existence of Nash equilibria for decentralized control schemes is introduced. This approach is based on directly proving the existence of a fixed point of the best reply correspondence of the underlying game. For the investigated flow control model, the best reply correspondence is shown to be a function, implicitly defined by means of $\textit{K}$ interdependent linear programs. Employing an appropriate definition for continuity of the set of optimal solutions of parameterized linear programs, it is shown that, under appropriate conditions, the best reply function is continuous. Brouwer's theorem implies, then, that the best reply function has a fixed point. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1995-05-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 42 Issue Number 3 Page Count 30 Starting Page 584 Ending Page 613

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Source: ACM Digital Library