In mathematics, a supermodular function is a function on a lattice that, informally, has the property of being characterized by "increasing differences...

nonnegative function on it, that is assumed to satisfy the (FKG) lattice condition (sometimes a function satisfying this condition is called log supermodular) i...

coverage. Supermodular function Matroid, Polymatroid Utility functions on indivisible goods H. Lin and J. Bilmes, A Class of Submodular Functions for Document...

Indeed, they show that their concept of quasi-supermodularity (a generalization of supermodular function) along with the single-crossing property, is necessary...

possible utility function for this case is given at the right. A utility function is additive if and only if it is both submodular and supermodular. Subadditivity...

effect – Sunk costs – Sunspot equilibrium – Sunspots (economics) – Supermodular function – Supply and demand – Supply-side economics – Surplus value – Sustainable...

a feature of the environment changes. The result states that if f is supermodular in (x,θ), and D is a lattice, then x ∗ ( θ ) = arg ⁡ max x ∈ D f ( x...

{\displaystyle i\neq j} . Equivalently, this means that the function Π {\displaystyle \,\Pi } is supermodular. On the other hand, the decisions are strategic substitutes...

Specifically, a game is convex if its characteristic function v {\displaystyle v} is supermodular: v ( S ∪ T ) + v ( S ∩ T ) ≥ v ( S ) + v ( T ) , ∀  ...

applications to supermodular games. A supermodular game (also called a game of strategic complements) is a game in which the utility function of each player...

f(x)-f(x\wedge x').} Every supermodular function is quasisupermodular. As in the case of single crossing differences, and unlike supermodularity, quasisupermodularity...

utility functions is weakly additive. A utility function is additive if and only if it is both submodular and supermodular. Utility functions on indivisible...

Submodular fuzzy measures result in convex functions, while supermodular fuzzy measures result in concave functions when used to define a Choquet integral...

{\displaystyle X} is a deterministic function of Y {\displaystyle Y} and Y {\displaystyle Y} is a deterministic function of X {\displaystyle X} then all information...

submodular function f {\displaystyle f} such that f ( ∅ ) = 0 {\displaystyle f(\emptyset )=0} and E P f = E P {\displaystyle EP_{f}=EP} . For a supermodular f...

upper-bounded supermodular set functions.: Lem.1.3.3  In a non-bipartite graph, the deficiency function is, in general, not supermodular. A graph G has...

No-trade theorem, Market design, Reputation effects (game theory), supermodular games, monotone comparative statics, Linkage principle, Deferred-acceptance...

The method uses lattice theory and introduces the notions of quasi-supermodularity and the single-crossing condition. The wide application of monotone...

complementarity is due to Masahiko Aoki and relies on the theory of supermodular games developed by Paul Milgrom and John Roberts. The basic structure...

valuations. When agents' utilities are superadditive set functions (more general than supermodular), a ( log ⁡ m ) 1 + ϵ m {\displaystyle {\frac {(\log m)^{1+\epsilon...

lattice-theoretic methods to analyze games of strategic complementarities (or supermodular games), and in general complementarities, in economics. His contribution...