Non-cooperative games with minmax objectives
The authors consider noncooperative games where each player's penalty function is composite, with the second term being a common nonsmooth function, which is supposed to be given by a max-type one. They propose two ways to treat this problem. Firstly, they replace it with the enlarged one, where the common term is transferred to an additional player with the corresponding smooth payoff function, thus removing the maximum operation. Secondly, they suggest a smoothing approximation of the common term, which gives a parametric family of Nash equilibrium problems. Convergence results for the general best response algorithm are given. Its diagonalized versions are also discussed.
scientific article; zbMATH DE number 6345667
scientific article