Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best Response
- Resource Type
- Authors
- Sonja Steffensen; Anna Thünen; Michael Herty
- Source
- Subject
- TheoryofComputation_MISCELLANEOUS
0209 industrial biotechnology
Class (set theory)
Computer Science::Computer Science and Game Theory
Control and Optimization
Mathematics::Optimization and Control
0211 other engineering and technologies
02 engineering and technology
FOS: Economics and business
Statistics::Machine Learning
symbols.namesake
020901 industrial engineering & automation
Quadratic equation
Economics - Theoretical Economics
FOS: Mathematics
Mathematics - Optimization and Control
Mathematics
91A06, 91A10, 90C33, 91A65, 49J52
021103 operations research
Applied Mathematics
TheoryofComputation_GENERAL
Statistics::Computation
Nash equilibrium
Optimization and Control (math.OC)
Best response
symbols
Theoretical Economics (econ.TH)
Leader follower
Mathematical economics
Game theory
Software
Smoothing
- Language
We derive 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 fulfill 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.