- R k → R {\displaystyle f\colon \mathbb {R} ^{k}\to \mathbb {R} } is
supermodular if f ( x ↑ y ) + f ( x ↓ y ) ≥ f ( x ) + f ( y ) {\displaystyle f(x\uparrow...
- queries. Tarski's fixed-point
theorem has
applications to
supermodular games. A
supermodular game (also
called a game of
strategic complements) is a game...
- case. A
typical utility function for this case is
given at the right.
Supermodularity is the
opposite of submodularity: it
means that "the
whole is not less...
- Equivalently, this
means that the
function Π {\displaystyle \,\Pi } is
supermodular. On the
other hand, the
decisions are
strategic substitutes if ∂ 2 Π...
-
condition (sometimes a
function satisfying this
condition is
called log
supermodular) i.e., μ ( x ∧ y ) μ ( x ∨ y ) ≥ μ ( x ) μ ( y ) {\displaystyle \mu (x\wedge...
- conditions. Indeed, they show that
their concept of quasi-
supermodularity (a
generalization of
supermodular function)
along with the single-crossing property...
- game is
convex if its
characteristic function v {\displaystyle v} is
supermodular: v ( S ∪ T ) + v ( S ∩ T ) ≥ v ( S ) + v ( T ) , ∀ S , T ⊆ N . {\displaystyle...
- ∪ F ) = g ( E ) + g ( F ) . {\displaystyle g(E\cup F)=g(E)+g(F).} ;
supermodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have...
-
other hand, they
model notions of diversity,
information and coverage.
Supermodular function Matroid,
Polymatroid Utility functions on
indivisible goods...
- No-trade theorem,
Market design, Re****tion
effects (game theory),
supermodular games,
monotone comparative statics,
Linkage principle, Deferred-acceptance...
