Solving quadratic multi-leader-follower games by smoothing the follower's best response.

Autor:	Herty, Michael, Steffensen, Sonja, Thünen, Anna
Předmět:	NASH equilibrium SUBGRADIENT methods NEWTON-Raphson method GAMES GAME theory QUASI-Newton methods
Zdroj:	Optimization Methods & Software; Apr2022, Vol. 37 Issue 2, p772-799, 28p
Abstrakt:	We analyse the existence of Nash equilibria for a class of quadratic multi-leader-follower games using the nonsmooth best response function. To overcome the challenge of nonsmoothness, we pursue a smoothing approach resulting in a reformulation as a smooth Nash equilibrium problem. The existence and uniqueness of solutions are proven for all smoothing parameters. Accumulation points of Nash equilibria exist for a decreasing sequence of these smoothing parameters and we show that these candidates fulfil the conditions of S-stationarity and are Nash equilibria to the multi-leader-follower game. Finally, we propose an update on the leader variables for efficient computation and numerically compare nonsmooth Newton and subgradient methods. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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