Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games

By J. Goodman. 1965

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Citations in the corpus

GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium (2019, background): “To discover a form of Nash equilibrium in such an environment is analogous to fixing a problem with inequality in variations with the help of a monotone operator (Harker & Pan, 1990; Rosen, 1965).”
Power control in two-tier femtocell networks (2008, methodology): “We now employ the following theorem from Glicksberg [38], Rosen [ 39 ] and Debreu [40]:”
A class of gap functions for quasi-variational inequality problems (2007, methodology): “type function methods would also be worth investigation [ 15 , 12, 5, 17, 13].”
Gap Function Approach to the Generalized Nash Equilibrium Problem (2010, methodology): “1 In [ 12 ], the concept of diagonal strict concavity is introduced, since each player is supposed to solve a”
Optimal and autonomous incentive-based energy consumption scheduling algorithm for smart grid (2010, result): “In this case, the existence of a Nash equilibrium directly results from [16, Theorem 1]. Moreover, the Nash equilibrium is unique due to [ 16, Theorem 3 ].”
Variational Inequality Models of Restructured Electricity Systems (2001, background): “It is possible to analyse the equilibria achievable when there are transmission constraints but no market for transmission services by resorting to the notion of generalized equilibrium (Rosen (1965)).”
Generalized Nash equilibrium problems (2007, unknown): “The main interest of ODE methods is historical, since they were first proposed in the influential paper ( Rosen 1965 ).”
Game Theory in Supply Chain Analysis (2004, result): “Proof of this result can be found in [41] and some further developments that deal with boundary equilibria are found in [ 80 ].”