Relaxation algorithms to find Nash equilibria with economic applications

By J. Krawczyk, Stanislav Uryasev. 2000

230 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Economics and Econometrics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ba57007da9320450540eb9f38429e0ad86240b61

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Citations in the corpus

Gap Function Approach to the Generalized Nash Equilibrium Problem (2010, background): “many applications such as electric power models [14, 19] and river basin pollution games [12, 15, 16 ].”
Generalized Nash equilibrium problems (2007, unknown): “…that uses the recursion xk+1 := (1− tk)xk + tk yk, where yk is an element of the set Ŷ(xk) defined in (8) and where the stepsize tk satisfies the conditions tk ∈ (0, 1] ∀k ∈ N, tk → 0, ∞∑ k=0 tk = ∞, or (Krawczyk and Uryasev 2000) the (optimal) choice tk := arg min t∈(0,1] V̂ ( (1− t)xk + t yk).”
Sequential Estimation of Structural Models with a Fixed Point Constraint (2008, unknown): “5 Ba sar (1987) and Krawczyk and Uryasev (2000) apply the relaxation method to nd a Nash equilibrium of a game.”
Dynamic Games in the Economics and Management of Pollution (2009, background): “For a survey of numerical solutions to normalized equilibrium problems, see [131], and for their computations, see [132].”
Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets (2004, background): “…form) is defined as a three-tuple , where is the set of players; , , is the set of strategies (or strategy space) of player ; and , is the payoff (or welfare, utility, profit, etc.) function of player that assigns a real number to each element of the Cartesian product of the strategy spaces .”
Exact penalty functions for generalized Nash problems (2006, background): “On the other hand there is certainly a wealth of interesting applications that call for the solution of GNEPs: see, as a way of example, [4,10, 13 ,17,18]”