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On convergent subsequences of functions that are locally of bounded total variation
In mathematics, Helly's selection theorem (also called the Helly selection principle) states that a uniformly bounded sequence of monotone real functions
Helly's_selection_theorem
On convergent subsequences of regulated functions
In mathematics, the Fraňková–Helly selection theorem is a generalisation of Helly's selection theorem for functions of bounded variation to the case of
Fraňková–Helly selection theorem
Fraňková–Helly_selection_theorem
Mathematical method
analysis, a branch of mathematics, a selection theorem is a theorem that guarantees the existence of a single-valued selection function from a given set-valued
Selection_theorem
Austrian mathematician (1884–1943)
Eduard Helly (June 1, 1884 in Vienna – 28 November 1943 in Chicago) was a mathematician after whom Helly's theorem, Helly families, Helly's selection theorem
Eduard_Helly
On when a family of real, continuous functions has a uniformly convergent subsequence
{\displaystyle C([0,T],L^{1}(\mathbb {R} ^{N})).} Helly's selection theorem Fréchet–Kolmogorov theorem Arzelà, Cesare (1895), "Sulle funzioni di linee"
Arzelà–Ascoli_theorem
Green's theorem (vector calculus) Helly's selection theorem (mathematical analysis) Implicit function theorem (vector calculus) Increment theorem (mathematical
List_of_theorems
measure. By a compactness argument (or equivalently in this case Helly's selection theorem for Stieltjes integrals), a subsequence of these probability measures
Positive_harmonic_function
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no procedure for group
Arrow's_impossibility_theorem
space, then Reg([0, T]; X) satisfies a compactness theorem known as the Fraňková–Helly selection theorem. The set of discontinuities of a regulated function
Regulated_function
Gives condition for a set of functions to be relatively compact in an Lp space
x}}=0,\quad u(x,0)=u_{0}(x).} Arzelà–Ascoli theorem Helly's selection theorem Rellich–Kondrachov theorem Sudakov, V. N. (1957). "Criteria of compactness
Fréchet–Kolmogorov_theorem
Theorem in functional analysis
by the Riesz representation theorem), the sequential Banach–Alaoglu theorem is equivalent to the Helly selection theorem. Proof For every x ∈ X , {\displaystyle
Banach–Alaoglu_theorem
σ-finite measure, but the converse is again not true. Helly's selection theorem Helly–Bray theorem Klenke, Achim (2008). Probability Theory. Berlin: Springer
Sub-probability_measure
In board games that cannot end in a draw, one of the two players has a winning strategy
In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which
Zermelo's theorem (game theory)
Zermelo's_theorem_(game_theory)
Real function with finite total variation
Renato Caccioppoli Caccioppoli set Lamberto Cesari Ennio De Giorgi Helly's selection theorem Locally integrable function Lp(Ω) space Lebesgue–Stieltjes integral
Bounded_variation
Combinatorial game theory theorem
In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap
Sprague–Grundy_theorem
Weakly optimal allocation of resources
asymmetric information, signalling, adverse selection, and moral hazard are introduced, most people do not take the theorems of welfare economics as accurate descriptions
Pareto_efficiency
Class of theorems about Nash equilibrium payoff profiles in repeated games
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games (Friedman 1971). The
Folk_theorem_(game_theory)
Logical paradox in decision-making theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Paradox_of_tolerance
Application of game theory to evolving populations in biology
distribution. The distribution (an ESS) can be computed using the Bishop-Cannings theorem, which holds true for any mixed-strategy ESS. The distribution function
Evolutionary_game_theory
Pairing where no unchosen pair prefers each other over their choice
and hybrid CPU–GPU execution to reduce overhead. The rural hospitals theorem concerns a more general variant of the stable matching problem, like that
Stable_matching_problem
Condition in economics and game theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Perfect_information
Hungarian and American mathematician and physicist (1903–1957)
the application of this work was instrumental in his mean ergodic theorem. The theorem is about arbitrary one-parameter unitary groups t → V t {\displaystyle
John_von_Neumann
Solution concept of a non-cooperative game
players. See also: Minimax theorem – Gives conditions that guarantee the max–min inequality holds with equality Equilibrium selection - explains how players
Nash_equilibrium
Subfield of set theory
This fact—that all closed games are determined—is called the Gale–Stewart theorem. Note that by symmetry, all open games are determined as well. (A game
Determinacy
Field of economics and game theory
described by Noam Nisan as a way to escape the Gibbard–Satterthwaite theorem. While the theorem is traditionally presented as a result about voting systems, it
Mechanism_design
Concept in game theory
ranked voting with three or more alternatives (by the Gibbard–Satterthwaite theorem) or first-price auctions. A randomized mechanism is a probability-distribution
Incentive_compatibility
Problem about bus travel
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Wait/walk_dilemma
Mathematical models of strategic interactions
von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard
Game_theory
Paper-and-pencil game for two players
successful landing and must be careful not to block themself. Hales–Jewett theorem m,n,k-game Number Scrabble Garcia, Dan. "GamesCrafters: Tic-Tac-Toe". gamescrafters
Tic-tac-toe
Theorem in game theory
Aumann's agreement theorem states that two Bayesian agents with the same prior beliefs cannot "agree to disagree" about the probability of an event if
Aumann's_agreement_theorem
Solution concept in game theory
(1995) retracted this conclusion to take risk dominance as the relevant selection criterion. Samuel Bowles: Microeconomics: Behavior, Institutions, and
Risk_dominance
Game mechanic where players act at the same time
Simultaneous action selection, or SAS, is a game mechanic that occurs when players of a game take action (such as moving their pieces) at the same time
Simultaneous_action_selection
Model of conflict for two players in game theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Chicken_(game)
Hand game for two or more players
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Chopsticks_(hand_game)
Mathematical modelling of phenotypic evolution
population swiftly goes extinct. The basic principles of evolution via natural selection were outlined by Charles Darwin in his 1859 book, On the Origin of Species
Evolutionary invasion analysis
Evolutionary_invasion_analysis
Hand game for two players or more
settle a dispute or make an unbiased group decision. Unlike truly random selection methods, however, rock paper scissors can be played with some degree of
Rock_paper_scissors
English saying meaning "equivalent retaliation"
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Tit_for_tat
Situation where all parties are worse off
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
No-win_situation
Military strategy during the Cold War with regard to the use of nuclear weapons
e12350. doi:10.1111/dome.12350. ISSN 1949-3606. Fearon, James (2002). "Selection Effects and Deterrence". International Interactions. 28 (1): 5–29. doi:10
Deterrence_theory
the outcomes associated. A commonly used theorem in relation to outcomes is the Nash equilibrium. This theorem is a combination of strategies in which
Outcome_(game_theory)
Branch of game theory about two-player sequential games with perfect information
that a player who cannot move loses. In the 1930s, the Sprague–Grundy theorem showed that all impartial games are equivalent to heaps in Nim, thus showing
Combinatorial_game_theory
Israeli psychologist (1937–1996)
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Amos_Tversky
Game theory concept
Centipede game Dynamic inconsistency Glossary of game theory Minimax theorem Retrograde analysis Solution concept Bellman's principle of optimality
Subgame_perfect_equilibrium
Academic discipline
often-cited paper describing experiments which could be used to prove Bell's theorem. In one part of this paper, they describe a game where a player could have
Quantum_game_theory
Facilitating a peaceful outcome to a dispute
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Conflict_resolution
Search algorithm
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Alpha–beta_pruning
Israeli-American psychologist and economist (1934–2024)
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Daniel_Kahneman
Journal of Economic Theory 68, 258–265. Nachbar, J. (1990) "Evolutionary Selection Dynamics in Games: Convergence and Limit Properties", International Journal
Fictitious_play
Tendency to overestimate in auctions
curse when bidding (an outcome that, according to the revenue equivalence theorem, need never occur). The winner's curse phenomenon was first addressed in
Winner's_curse
Game whose outcome can be correctly predicted
Computer Go Computer Othello Game complexity God's algorithm Zermelo's theorem (game theory) Allis, L.V. (1994). Searching for solutions in games and
Solved_game
Concept in game theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Shapley_value
Concept in conflict studies
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Conflict_escalation
Diplomatic policy of concessions
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Appeasement
Concept in game theory
Coordination game Simultaneous game Surprisingly popular Equilibrium selection Rendezvous problem, the mathematical problem of maximising the probability
Focal_point_(game_theory)
Concept in game theory
Equilibrium selection is a concept from game theory which seeks to address reasons for players of a game to select a certain equilibrium over another
Equilibrium_selection
Game theory model of aggression
of the competing individuals. Evolutionary game theory Bishop–Cannings theorem Rubinstein bargaining model Hawk-dove game Dollar auction Attrition warfare
War_of_attrition_(game)
American economist (born 1948)
inventions of new auction formats". He is the co-creator of the no-trade theorem with Nancy Stokey. He is the co-founder of several companies, the most
Paul_Milgrom
Field in social science
mechanisms are less likely to be published. After accounting for publication selection bias, the analysis finds that, on average, income-increasing shocks in
Peace_and_conflict_studies
Mixed strategy equilibria explained as the limit of pure strategy equilibria
In game theory, the purification theorem was contributed by Nobel laureate John Harsanyi in 1973. The theorem justifies a puzzling aspect of mixed strategy
Purification_theorem
Concept in game theory
finding a Nash equilibrium by computing the best response for every player: Theorem—In any finite potential game, best response dynamics always converge to
Best_response
Conflict between safety and cooperation
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Stag_hunt
Two player pursuit-evasion problem
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Princess_and_monster_game
Solution concept in game theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Proper_equilibrium
Game theory concept
type of a player is treated as a separate "player." This is detailed in Theorem 9.51 of the book Game Theory. Induced Normal Form Game: The number of players
Bayesian_game
Point in evolutionary space where selection always leads
An evolutionary attractor is a point in an evolutionary space where a selection process will always drive trait values towards that point from the region
Evolutionary_attractor
Hungarian-American economist and philosopher (1920–2000)
utilitarian ethics) as well as contributing to the study of equilibrium selection. For his work, he was a co-recipient along with John Nash and Reinhard
John_Harsanyi
Game where groups of players may enforce cooperative behaviour
of winning coalitions with empty intersection. According to Nakamura's theorem, the number measures the degree of rationality; it is an indicator of the
Cooperative_game_theory
Subset of a game; used in game theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Subgame
Standard example in game theory
Abilene paradox Centipede game Collective action problem Externality Folk theorem (game theory) Free-rider problem Gift-exchange game Hobbesian trap Innocent
Prisoner's_dilemma
Game-theoretic concept
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Cheap_talk
Political model of international conflict resolution
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Two-level_game_theory
Situation where total gains match total losses
non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, or with Nash equilibrium
Zero-sum_game
Concept in economics and game theory
relevant fundamentals with small noise, and show that this leads to the selection of a unique equilibrium. This result overturns the result in models of
Global_game
Concept in game theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Non-credible_threat
Class of strategies employed in a repeated non-cooperative game
A non-cooperative equilibrium for supergames, Review of Economic Studies 38, 1–12. (The first formal proof of the Folk theorem (game theory)). v t e
Trigger_strategy
Process of reasoning backwards in sequence
the related fields of automated planning and scheduling and automated theorem proving, the method is called backward search or backward chaining. In
Backward_induction
Human behavior pattern in which the participant takes on increasing risk
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Escalation_of_commitment
Complete plan on how a game player will behave in every possible game situation
relationship between mixed and behavior strategies is the subject of Kuhn's theorem, a behavioral outlook on traditional game-theoretic hypotheses. The result
Strategy_(game_theory)
Quality of a strategy in game theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Strategic_dominance
Solution to the fair division problem
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Moving-knife_procedure
Overuse of a shared resource
environmental conditions, they mostly are filtered out (die) by environmental selection; hence, populations in hostile conditions are selected to be cooperative
Tragedy_of_the_commons
Formal rule for predicting how a game will be played
alludes to the fact that players update their beliefs according to Bayes' theorem. They calculate probabilities given what has already taken place in the
Solution_concept
Making of satisfactory, not optimal, decisions
incompatibility (help) Simon, Herbert (1990). "A mechanism for social selection and successful altruism". Science. 250 (4988): 1665–8. Bibcode:1990Sci
Bounded_rationality
Polish-American mathematician (1911-1992)
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Melvin_Dresher
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Strategic_move
Dynamical system
non-linear, and non-innovative dynamic that captures the principle of natural selection in strategic interactions. The replicator equation describes how strategies
Replicator_equation
Economic Model
will exist when there are convex costs. Dixon’s proof used the Existence Theorem of Partha Dasgupta and Eric Maskin. Under Dixon's assumption of (weakly)
Bertrand–Edgeworth_model
Decision rule used for minimizing the possible loss for a worst-case scenario
important in the theory of repeated games. One of the central theorems in this theory, the folk theorem, relies on the minimax values. In combinatorial game theory
Minimax
Level of information in economics and game theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Complete_information
Preference of known risks to unknown risks
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Ambiguity_aversion
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Implementation_theory
Concept in economics and game theory
inequality ( x − y / 2 ) 2 ≥ 0 {\displaystyle (x-y/2)^{2}\geq 0} . Q.E.D. Theorem. The pure PoA of any generalized routing problem ( G , L ) {\displaystyle
Price_of_anarchy
Cooperation between firms to limit competition
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Collusion
Economic model
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Stackelberg_competition
Model of humans as rational, self-interested agents
greatly exceeded that of the WTP. This was seen as falsifying the Coase theorem in which for every person the WTA equals the WTP that is the basis of the
Homo_economicus
Study of strategic decision making
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Mean-field_game_theory
Israeli-American mathematician (born 1930)
Shapley on the Aumann–Shapley value. He is also known for Aumann's agreement theorem, in which he argues that under his given conditions, two Bayesian rationalists
Robert_Aumann
Principle in economics and game theory
system or market). It can be seen as a kind of mirror image to Gibbard's theorem. The revelation principle says that if a social choice function can be
Revelation_principle
Simultaneous game found in game theory
decision-making Cooperative game Coordination failure (economics) Equilibrium selection Focal point Guess 2/3 of the average Non-cooperative game Self-fulfilling
Coordination_game
Economic model
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Cournot_competition
HELLYS SELECTION-THEOREM
HELLYS SELECTION-THEOREM
Boy/Male
Muslim
Selection, Choice
Boy/Male
American, Australian, British, English, Jamaican
Hero; Holly-tree Grove; Lives Near the Holly Trees
Girl/Female
Christian & English(British/American/Australian)
The Holly Bush
Girl/Female
Australian, British, English
Form of Holly; Holly Grove
Girl/Female
American, Anglo, Australian, British, Chinese, Christian, Danish, English, French, German, Irish, Jamaican
To Prick; Holly Grove; Shrub with Red Berries; Evergreen
Surname or Lastname
English
English : probably a variant of Helms.
Female
Finnish
 Short form of Finnish Helleena, probably HELLE means "torch." Compare with other forms of Helle.
Female
Icelandic
 Dialectal variant form of Icelandic Helga, HELLA means "holy; dedicated to the gods." Compare with another form of Hella.
Male
Greek
(á¼Î»Î¹Î¿Ï‚) Greek name HELIOS means "sun." In mythology, this is the name of a sun god.
Girl/Female
English
The holly tree. Common name given Christmas girl babies.
Boy/Male
Arabic, Muslim, Sindhi
Selection; Choice
Female
English
Variant spelling of English Helen, probably HELLEN means "torch."
Female
Finnish
Finnish name HELLÄ means "gentle."
Female
German
 Pet form of German Helene, probably HELLA means "torch." Compare with another form of Hella.
Male
English
Anglicized unisex form of Irish Gaelic Ceallach, KELLY means "bright-headed."
Girl/Female
American, Australian, British, English, Jamaican
Lives Near the Holly Trees
Girl/Female
American, Hindu, Indian
Selection
Surname or Lastname
English
English : topographic name for someone who lived in a place where there was more than one mill, Middle English melles ‘mills’, or habitational name for someone from Mells in Somerset, named with this word.
Boy/Male
English American
Lives by the holly trees.
Surname or Lastname
English
English : variant of Helms. This name occurs predominantly in SC.
HELLYS SELECTION-THEOREM
HELLYS SELECTION-THEOREM
Boy/Male
Indian, Kannada, Tamil
God Sivan
Girl/Female
Arabic, Muslim, Sindhi
Religious; Righteous Woman
Female
Native American
Native American Algonquin name MAKKITOTOSIMEW means "she has large breasts."
Girl/Female
Arabic, Muslim
Prosperity
Boy/Male
Indian, Sanskrit
A Sacred Chant; Verse; Hindu Prayer
Boy/Male
British, English
From the White Hollow
Girl/Female
Norse American
Fate.
Boy/Male
Tamil
Shrimath | à®·à¯à®°à¯€à®®à®¾à®¤Â
Auspicious, Lord Vishnu, Revered
Girl/Female
Arabic, Muslim
Bright
Boy/Male
Finnish, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
High; Tall
HELLYS SELECTION-THEOREM
HELLYS SELECTION-THEOREM
HELLYS SELECTION-THEOREM
HELLYS SELECTION-THEOREM
HELLYS SELECTION-THEOREM
n.
A part reflected, or turned back, at an angle; as, the reflection of a membrane.
n.
Election a second time, or anew; as, the reelection of a former chief.
n.
A lesson or selection, esp. of Scripture, read in divine service.
n.
The act of selecting, or the state of being selected; choice, by preference.
a.
Hellish.
n.
Jelly.
a.
Abounding with shells; consisting of shells, or of a shell.
n.
That which is produced by reflection.
n.
That which is selected; a collection of things chosen; as, a choice selection of books.
n.
That portion of a group of moldings which projects beyond the general surface of a panel; a bolection.
a.
The act of choosing; choice; selection.
n.
The act of detecting; the laying open what was concealed or hidden; discovery; as, the detection of a thief; the detection of fraud, forgery, or a plot.
a.
Abounding with hills; uneven in surface; as, a hilly country.
n.
The act of cutting, or separation by cutting; as, the section of bodies.
a.
The act of choosing a person to fill an office, or to membership in a society, as by ballot, uplifted hands, or viva voce; as, the election of a president or a mayor.
n.
A projecting molding round a panel. Same as Bilection.
n.
The return of rays, beams, sound, or the like, from a surface. See Angle of reflection, below.
pl.
of Selectman
a.
Selecting; tending to select.
n.
An election held by itself, not at the time of a general election.