This exploration of a complete order enhances equilibrium definition in noncooperative games, suggesting efficient optimization strategies.
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.
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Setiawan et al. (2025) studied this question.
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