These notes develop the theory of supermodular games. Supermodular games are those characterized by “strategic complementarities” – roughly, this means that when one player takes a higher action, the others want to do the same. Supermodular games are interesting for several reasons. First, they encompass many applied models. Second, they have the remarkable property that many solution concepts ...

The modular transformations of the (1|1) complex supermanifolds in the likeSchottky modular parameterization are discussed. It is shown that these ”supermodular” transformations depend on the spinor structure of the (1|1) complex supermanifold by terms proportional to the odd modular parameters. The above terms are calculated in the explicit form. The discussed terms are important for the study...

Supermodular games are an interesting class of games that exhibits strategic complementarity. There are several compelling reasons like existence of pure strategy nash equilibrium, dominance solvability, identical bounds on joint strategy space etc. that make them a strong candidate for game theoretic modeling of economics. Supermodular games give a sound framework for analysis as it is based o...

Coalitional games allow subsets (coalitions) of players to cooperate to receive a collective payoff. This payoff is then distributed “fairly” among the members of that coalition according to some division scheme. Various solution concepts have been proposed as reasonable schemes for generating fair allocations. The Shapley value is one classic solution concept: player i’s share is precisely equ...

A sublattice in a lattice is called supermodular if, for every two elements, one of which belongs to the sublattice, at least one of their meet and join also belongs to the sublattice. In this note, we describe supermodular sublattices in products of relatively complemented lattices.