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Dynamical system
In mathematics, the replicator equation is a type of dynamical system used in evolutionary game theory to model how the frequency of strategies in a population
Replicator_equation
Topics referred to by the same term
Look up replicator in Wiktionary, the free dictionary. Replicator may refer to: Replicator (evolution unit), the theoretical basic unit of evolution in
Replicator
Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical
List_of_equations
Set of equations
coefficients, is available, which is based upon equivalence to the 3-type replicator equation. In the case of a single trophic community, the trophic level below
Generalized Lotka–Volterra equation
Generalized_Lotka–Volterra_equation
Paper-and-pencil game for two players
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Tic-tac-toe
Application of game theory to evolving populations in biology
the population and how the less fit will be culled, in a replicator equation. The replicator dynamics models heredity but not mutation, and assumes asexual
Evolutionary_game_theory
Hungarian and American mathematician and physicist (1903–1957)
this work he wrote a paper with A. H. Taub and Veblen extending the Dirac equation to projective relativity, with a key focus on maintaining invariance with
John_von_Neumann
Standard example in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Prisoner's_dilemma
Hand game for two players or more
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Rock_paper_scissors
Weakly optimal allocation of resources
ui(s) for every player i and uj(s′) > uj(s) for some player j. In this equation, u represents the utility or benefit and j represents the player. Efficiency
Pareto_efficiency
Model of conflict for two players in game theory
"anti-property rights" one must discover a way to break this additional symmetry. Replicator dynamics is a simple model of strategy change commonly used in evolutionary
Chicken_(game)
Condition where selection restores genetic composition
the replicator equation is also a frequently utilized tool. Evolutionarily stable states are often taken as solutions to the replicator equation, here
Evolutionarily_stable_state
Logical paradox in decision-making theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Paradox_of_tolerance
Economic model
{\displaystyle m_{1}} of the first equation is necessarily greater than the root m 2 {\displaystyle m_{2}} of the second equation. We have seen that Cournot's
Cournot_competition
Solution concept of a non-cooperative game
strategy of a particular player should be 1. This creates a system of equations from which the probabilities of choosing each strategy can be derived
Nash_equilibrium
Israeli-American psychologist and economist (1934–2024)
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Daniel_Kahneman
Description of how a trait or gene changes in frequency over time
the second term is zero, we get the replicator equation, which is the continuous analogue of the simple Price equation below. When the characteristic values
Price_equation
Mathematical models of strategic interactions
rule explains the evolutionary rationale behind this selection with the equation c < b × r, where the cost c to the altruist must be less than the benefit
Game_theory
Fictional machine in the Star Trek universe
</noinclude> In Star Trek, a replicator is a machine that can create (and recycle) things. Replicators were originally seen to simply synthesize meals
Replicator_(Star_Trek)
Overuse of a shared resource
destruction of the file in the digital environment, and because it can be replicated and disseminated throughout the digital environment. However, it can still
Tragedy_of_the_commons
Finding an optimal algorithm for playing chess
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Solving_chess
Diplomatic policy of concessions
to defend Czechoslovakia in the event of war and the exclusion from the equation of the Soviet Union, which Chamberlain distrusted, meant that the outcome
Appeasement
proximity. This assumption is implicit in the replicator equation, a system of differential equations that represents one of the fundamental models in
Complete_mixing
Model of multi-species population dynamics
coefficients, is available, which is based upon equivalence to the 3-type replicator equation. This model can be generalized to any number of species competing
Competitive Lotka–Volterra equations
Competitive_Lotka–Volterra_equations
Model of humans as rational, self-interested agents
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Homo_economicus
Facilitating a peaceful outcome to a dispute
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Conflict_resolution
Game in experimental economics
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Impunity_game
Decision rule used for minimizing the possible loss for a worst-case scenario
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Minimax
Search algorithm
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Alpha–beta_pruning
Cyclic sequence of self-reproducing single cycles
all essential information. The hypercycle is a special case of the replicator equation. The most important properties of hypercycles are autocatalytic growth
Hypercycle_(chemistry)
English saying meaning "equivalent retaliation"
An agent using this strategy will first cooperate, then subsequently replicate an opponent's previous action. If the opponent previously was cooperative
Tit_for_tat
Making of satisfactory, not optimal, decisions
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Bounded_rationality
Concept in game theory
natural "focal point". Later, Schelling's informal experiments have been replicated under controlled conditions with monetary incentives by Judith Mehta.
Focal_point_(game_theory)
Problem in process of sharing surplus
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Cooperative_bargaining
Military strategy during the Cold War with regard to the use of nuclear weapons
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Deterrence_theory
Term in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Move_by_nature
Hungarian-American economist and philosopher (1920–2000)
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
John_Harsanyi
Game in economic experiments
behavior in the ultimatum game. Simple evolutionary models, e.g. the replicator dynamics, cannot account for the evolution of fair proposals or for rejections
Ultimatum_game
Conflict between safety and cooperation
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Stag_hunt
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Contingent_cooperator
Israeli psychologist (1937–1996)
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Amos_Tversky
Game whose outcome can be correctly predicted
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Solved_game
Proof all ranked voting rules have spoilers
feelings-to-actions relationship takes a generic form, is consistently replicable, and is fairly close to linear in structure. Therefore, it seems that
Arrow's_impossibility_theorem
Situation where total gains match total losses
by using a change of variables that puts it in the form of the above equations and thus such games are equivalent to linear programs, in general. If
Zero-sum_game
Game theory scenario
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Win–win_game
Field of economics and game theory
\theta } the control. As usual in optimal control the costate evolution equation must satisfy ∂ ν ∂ θ = − ∂ H ∂ x = − ( ∂ V ∂ x ( x , θ ) − 1 − P ( θ )
Mechanism_design
Pairing where no unchosen pair prefers each other over their choice
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Stable_matching_problem
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Asynchrony_(game_theory)
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Implementation_theory
Iterated game for peace and conflict studies
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Peace_war_game
Quality of a strategy in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Strategic_dominance
Concept in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Shapley_value
Condition in economics and game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Perfect_information
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Strategic_move
Problem in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Airport_problem
Hand game for two or more players
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Chopsticks_(hand_game)
Situation where all parties are worse off
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
No-win_situation
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
List_of_games_in_game_theory
Political model of international conflict resolution
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Two-level_game_theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Uncorrelated_asymmetry
Type of signaling game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Lewis_signaling_game
Solution concept in Game Theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Bayes_correlated_equilibrium
Field in social science
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Peace_and_conflict_studies
Algorithm in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Paranoid_algorithm
Level of information in economics and game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Complete_information
Mathematical construct in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Hierarchy_of_beliefs
Branch of game theory about two-player sequential games with perfect information
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Combinatorial_game_theory
Austrian mathematician
(generalized Lotka–Volterra equation) on the plane, employing equivalence of this dynamics to the 3-type replicator equation. In “Non-cooperative two-person
Immanuel_Bomze
Game where groups of players may enforce cooperative behaviour
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Cooperative_game_theory
Mathematical game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Guess_2/3_of_the_average
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Coalition-proof Nash equilibrium
Coalition-proof_Nash_equilibrium
Modelling evolution using differential equations
evolutionary biology that developed from research using differential equations to model both genetic and phenotypic change. Thus it differs from population
Evolutionary_dynamics
Game with a stable optimal strategy
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Strictly_determined_game
Incomplete-information coordination game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Electronic_mail_game
Solution concept in Game Theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Cursed_equilibrium
Problem about bus travel
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Wait/walk_dilemma
Type of perfect Bayesian equilibrium
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Separating_equilibrium
Complete plan on how a game player will behave in every possible game situation
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Strategy_(game_theory)
Variation of minimax game tree search
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Negamax
Aspect of game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Self-confirming_equilibrium
Preference of known risks to unknown risks
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Ambiguity_aversion
Two-person zero-sum game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Search_game
Representation of a game in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Normal-form_game
Israeli-American mathematician (born 1930)
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Robert_Aumann
Two-player coordination game in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Battle of the sexes (game theory)
Battle_of_the_sexes_(game_theory)
Trigger strategy
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Grim_trigger
Game theory concept
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Game_form
Solution to the fair division problem
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Moving-knife_procedure
+ ϕ {\displaystyle \phi =-{\frac {1}{2+a+\phi }}} This is a quadratic equation which gives us the unique consistent conjecture ϕ ∗ = − ( 1 + a 2 ) + 4
Conjectural_variation
Game-theoretic concept
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Cheap_talk
Study of strategic decision making
Hamilton-Jacobi-Bellman equation is the Bellman equation, and the discrete version of the Fokker-Planck equation is the Kolmogorov equation. Specifically, for
Mean-field_game_theory
Bidding less than an item is worth in an auction
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Bid_shading
Strategy which only depends on the current state of a game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Markov_strategy
Resource distribution game
Play and Integral Equations with Skew Symmetric Kernels (1953 translation from the French paper "La théorie du jeu et les équations intégrales à noyau
Blotto_game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Fictitious_play
Concept in conflict studies
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Conflict_escalation
Study of strategic interactions on networks
These dynamics are the networked population version of the classical replicator equation for well-mixed populations. x ˙ = x ( 1 − x ) [ Π s 1 − Π s 2 ]
Game_theory_on_networks
Human behavior pattern in which the participant takes on increasing risk
Planck's principle – Principle that scientific change is generational Replication crisis – Observed inability to reproduce scientific studies Sunk cost –
Escalation_of_commitment
Game theory solution
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Correlated_equilibrium
Economic phenomenon
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Tyranny_of_small_decisions
REPLICATOR EQUATION
REPLICATOR EQUATION
Boy/Male
Hindu
Replicate
Boy/Male
Hindu, Indian
Replicate; Format
Boy/Male
Tamil
Praroop | பà¯à®°à®¾à®°à¯‚பÂ
Replicate
REPLICATOR EQUATION
REPLICATOR EQUATION
Boy/Male
American, British, English
Lives at the King's Spring; From the King's Well
Girl/Female
Farsi, Indian
Dream
Boy/Male
Hebrew
warrior.
Boy/Male
Tamil
Deep insight
Girl/Female
Tamil
Boy/Male
American, British, English, Teutonic
From the Fortress
Girl/Female
Greek Latin
Changed into a spider by Athena.
Boy/Male
Hindu
Sea or ocean
Girl/Female
Indian
Girl/Female
Indian, Telugu
Sweetness
REPLICATOR EQUATION
REPLICATOR EQUATION
REPLICATOR EQUATION
REPLICATOR EQUATION
REPLICATOR EQUATION
n.
An identical equation.
n.
The curve whose ordinates are proportional to the sines of the abscissas, the equation of the curve being y = a sin x. It is also called the curve of sines.
n.
The change, as of an equation or quantity, into another form without altering the value.
v. i.
To answer, as the defendant to the plaintiff's replication.
n.
An answer; a reply.
n.
The reply of the plaintiff, in matters of fact, to the defendant's plea.
n.
An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.
n.
The defendant's answer to the plaintiff's replication.
n.
The bringing of any term of an equation from one side over to the other without destroying the equation.
n.
The act of solving, or the state of being solved; the disentanglement of any intricate problem or difficult question; explanation; clearing up; -- used especially in mathematics, either of the process of solving an equation or problem, or the result of the process.
a.
To defeat or evade; to invalidate. Thus, in a replication, the plaintiff may deny the defendant's plea, or confess it, and avoid it by stating new matter.
a.
Recurring once a month; monthly; gone through in a month; as, the menstrual revolution of the moon; pertaining to monthly changes; as, the menstrual equation of the sun's place.
n.
One who unfolds or explains; an expounder; an explainer.
a.
Alt. of Replicated
n.
A quantity which may increase or decrease; a quantity which admits of an infinite number of values in the same expression; a variable quantity; as, in the equation x2 - y2 = R2, x and y are variables.
v. t.
To bring, as any term of an equation, from one side over to the other, without destroying the equation; thus, if a + b = c, and we make a = c - b, then b is said to be transposed.
n.
Return or repercussion, as of sound; echo.
v. t.
To reply.
a.
Folded over or backward; folded back upon itself; as, a replicate leaf or petal; a replicate margin of a shell.
n.
A repetition; a copy.