Recent Advances in Minimax Problem and Bimatrix Games

In this paper, we first survey recent developments in game theory, and then focus on minimax problems and bimatrix games. New optimality conditions for maxmin and minimax problems have been considered. Recently introduced new equilibriums such as Anti-Berge and Anti-Nash equilibriums are discussed with connection to optimization problems. We examine bimatrix games. Recent results in multi player polymatrix game have been given. The existence theorems of all equilibrium are provided. Also, a triple matrix game is introduced and existence of Nash equilibrium in the game has been established.