2018/08/23 by Michaël Herty, Herty, Michael, Sonja Steffensen +3
Decision Sciences · Medicine · Physics and Astronomy · #49J52 #90C33 #91A06 #91A10 #91A65 #FOS: Economics and business #FOS: Mathematics #Game Theory and Applications #Mathematical and Theoretical Epidemiology and Ecology Models #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.1808.07941
openalex publication_date 2018/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive Nash equilibria for a class of quadratic multi-leader-follower\ngames using the nonsmooth best response function. To overcome the challenge of\nnonsmoothness, we pursue a smoothing approach resulting in a reformulation as a\nsmooth Nash equilibrium problem. The existence and uniqueness of solutions are\nproven for all smoothing parameters. Accumulation points of Nash equilibria\nexist for a decreasing sequence of these smoothing parameters and we show that\nthese candidates fulfill the conditions of s-stationarity and are Nash\nequilibria to the multi-leader-follower game. Finally, we propose an update on\nthe leader variables for efficient computation and numerically compare\nnonsmooth Newton and subgradient methods.\n