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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
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
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
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
effect – Sunk costs – Sunspot equilibrium – Sunspots (economics) – Supermodular function – Supply and demand – Supply-side economics – Surplus value – Sustainable
Index_of_economics_articles
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
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
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
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
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
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
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)
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
SUPERMODULAR FUNCTION
SUPERMODULAR FUNCTION
Male
Egyptian
, an Egyptian functionary.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, a high Egyptian functionary.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, Functionary of the Interior.
Biblical
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Male
Egyptian
, a great functionary.
Male
Celtic
, great justiciary, or functionary.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Male
Egyptian
, the son of the functionary Heknofre.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
SUPERMODULAR FUNCTION
SUPERMODULAR FUNCTION
Boy/Male
Tamil
Satyaveer | ஸதà¯à®¯à®µà¯€à®°
Always speaking lie, Someone who gets victory with truth, Truthful
Girl/Female
Hindu
Bird, Hot
Boy/Male
Indian, Kannada, Tamil
Kind
Girl/Female
Indian, Tamil
Holiness; Happy; Jolly
Boy/Male
Arabic, Hindu, Indian, Kannada, Muslim, Oriya
Most Generous; Excellent; One who is without Karma
Boy/Male
Hindi
White.
Girl/Female
Anglo, Australian, British, English
Place Name; White Island
Female
Irish
Feminine form of Irish Gaelic Féidhlim, possibly FÉIDHELM means "hospitable." In Irish legend, this was the name of a daughter of Conchobhar.
Girl/Female
American, Christian, French, Indian
Dear or Beloved
Girl/Female
Muslim/Islamic
Name of a beautiful woman (wife of Murrah al-Asadi)
SUPERMODULAR FUNCTION
SUPERMODULAR FUNCTION
SUPERMODULAR FUNCTION
SUPERMODULAR FUNCTION
SUPERMODULAR FUNCTION
a.
Of, pertaining to, or designating, certain secret tribunals which flourished in Germany from the end of the 12th century to the middle of the 16th, usurping many of the functions of the government which were too weak to maintain law and order, and inspiring dread in all who came within their jurisdiction.
n.
A certain function relating to a system of forces and their points of application, -- first used by Clausius in the investigation of problems in molecular physics.
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
prep.
Acting as a substitute; -- said of abnormal action which replaces a suppressed normal function; as, vicarious hemorrhage replacing menstruation.
a.
Pertaining to the function of an organ or part, or to the functions in general.
a.
Belonging or relating to life, either animal or vegetable; as, vital energies; vital functions; vital actions.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
a.
Having relation to growth or nutrition; partaking of simple growth and enlargement of the systems of nutrition, apart from the sensorial or distinctively animal functions; vegetal.
a.
Pertaining to, or connected with, a function or duty; official.
n.
The doctrine that all the functions of a living organism are due to an unknown vital principle distinct from all chemical and physical forces.
v. i.
Alt. of Functionate
a.
Of or pertaining to the vessels of animal and vegetable bodies; as, the vascular functions.
v. i.
To execute or perform a function; to transact one's regular or appointed business.
n.
One deputed or authorized to perform the functions of another; a substitute in office; a deputy.
v. t.
To assign to some function or office.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
a.
Destitute of function, or of an appropriate organ. Darwin.
adv.
In a functional manner; as regards normal or appropriate activity.
pl.
of Functionary
n.
Fig.: Any cavity, or hollow place, in which any function may be conceived of as operating.