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Class of mathematical functions
In mathematics, a supermodular function is a function on a lattice that, informally, has the property of being characterized by "increasing differences
Supermodular_function
Correlation inequality
nonnegative function on it, that is assumed to satisfy the (FKG) lattice condition (sometimes a function satisfying this condition is called log supermodular) i
FKG_inequality
Set-to-real map with diminishing returns
coverage. Supermodular function Matroid, Polymatroid Utility functions on indivisible goods H. Lin and J. Bilmes, A Class of Submodular Functions for Document
Submodular_set_function
Theorem in mathematical economics
let D {\displaystyle D} be a lattice, and let f {\displaystyle f} be supermodular in x {\displaystyle x} and have increasing differences in ( x , θ ) {\displaystyle
Topkis's_theorem
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
Utility functions on indivisible goods
Utility_functions_on_indivisible_goods
American economist (born 1948)
Indeed, they show that their concept of quasi-supermodularity (a generalization of supermodular function) along with the single-crossing property, is necessary
Paul_Milgrom
Game theory concept
{\displaystyle i\neq j} . Equivalently, this means that the function Π {\displaystyle \,\Pi } is supermodular. On the other hand, the decisions are strategic substitutes
Strategic_complements
effect – Sunk costs – Sunspot equilibrium – Sunspots (economics) – Supermodular function – Supply and demand – Supply-side economics – Surplus value – Sustainable
Index_of_economics_articles
Game where groups of players may enforce cooperative behaviour
Specifically, a game is convex if its characteristic function v {\displaystyle v} is supermodular: v ( S ∪ T ) + v ( S ∩ T ) ≥ v ( S ) + v ( T ) , ∀
Cooperative_game_theory
f(x)-f(x\wedge x').} Every supermodular function is quasisupermodular. As in the case of single crossing differences, and unlike supermodularity, quasisupermodularity
Monotone_comparative_statics
Refinement of perfect matching theorems
properties of upper-bounded supermodular set functions. In a non-bipartite graph, the deficiency function is, in general, not supermodular. A graph G has the Hall
Deficiency_(graph_theory)
Theorem in order and lattice theory
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
Knaster–Tarski_theorem
Concept in economics
utility functions is weakly additive. A utility function is additive if and only if it is both submodular and supermodular. Utility functions on indivisible
Additive_utility
Measure of dependence between two variables
{\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
Mutual_information
Multiset analogue of matroids
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
Polymatroid
Theory of generalized measures in mathematics
Submodular fuzzy measures result in convex functions, while supermodular fuzzy measures result in concave functions when used to define a Choquet integral
Fuzzy_measure_theory
Thought experiments
The method uses lattice theory and introduces the notions of quasi-supermodularity and the single-crossing condition. The wide application of monotone
Comparative_statics
No-trade theorem, Market design, Reputation effects (game theory), supermodular games, monotone comparative statics, Linkage principle, Deferred-acceptance
List of Nobel Memorial Prize laureates in Economic Sciences
List_of_Nobel_Memorial_Prize_laureates_in_Economic_Sciences
Spanish economist (born 1955)
lattice-theoretic methods to analyze games of strategic complementarities (or supermodular games), and in general complementarities, in economics. His contribution
Xavier_Vives
Situations of interdependence among institutions
complementarity is due to Masahiko Aoki and relies on the theory of supermodular games developed by Paul Milgrom and John Roberts. The basic structure
Institutional_complementarity
valuations. When agents' utilities are superadditive set functions (more general than supermodular), a ( log m ) 1 + ϵ m {\displaystyle {\frac {(\log m)^{1+\epsilon
Welfare_maximization
Problem in mathematical sociology
which yields the rule in a Nash equilibrium. Moreover, for monotone and supermodular bilateral principles, every subgame perfect equilibrium is coalition-proof
Strategic_bankruptcy_problem
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