Complete lattice using lexicographical order and its application in non-cooperative ordered game

One application of lattices in optimization is defining the equilibrium set of ordered games, typically using the usual (coordinate-wise) order, which is incomplete in Rn. This incompleteness makes some strategies incomparable, requiring a special game concept. Using a complete order, like the lexicographic order, results in a complete lattice. This study explores the properties of a complete lattice with lexicographic order for noncooperative games and provides a Python algorithm to determine the Nash equilibrium of a supermodular game.