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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
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
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
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
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
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
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
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
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
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)
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
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
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
Fictional machine in the Star Trek universe
In Star Trek, a replicator is a machine that can create (and recycle) things. Replicators were originally seen to simply synthesize meals on demand, but
Replicator_(Star_Trek)
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
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
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
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
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
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
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
Search algorithm
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Alpha–beta_pruning
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
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)
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
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)
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
Game in experimental economics
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Impunity_game
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
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
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
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
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
Concept in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Shapley_value
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
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
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
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
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
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
Strategic_move
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
Problem in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Airport_problem
Israeli psychologist (1937–1996)
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Amos_Tversky
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
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)
Tendency to overestimate in auctions
report an effect size much larger than is likely to be seen in subsequent replication studies. Selection bias – Bias in a statistical analysis due to non-random
Winner's_curse
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
Game theory scenario
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Win–win_game
Term in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Move_by_nature
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Implementation_theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Transferable_utility
Game theory case weighing own/others' sacrifice
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Volunteer's_dilemma
Class of strategies employed in a repeated non-cooperative game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Trigger_strategy
American mathematician (1908-1991)
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Merrill_M._Flood
Israeli-American mathematician (born 1930)
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Robert_Aumann
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
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
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
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)
Game that repeats a base game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Repeated_game
Game theory concept
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Game_form
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
Class of games where players choose their actions sequentially
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Sequential_game
Type of signaling game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Lewis_signaling_game
Concept in conflict studies
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Conflict_escalation
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
List_of_games_in_game_theory
Problem about bus travel
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Wait/walk_dilemma
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
American economist
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
David_K._Levine
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Fictitious_play
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
Game class in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Screening_game
Analog of Pareto efficiency for situations with incomplete information
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Bayesian_efficiency
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
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)
Incomplete-information coordination game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Electronic_mail_game
Two-person zero-sum game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Search_game
proximity. This assumption is implicit in the replicator equation, a system of differential equations that represents one of the fundamental models in
Complete_mixing
Branch of mathematics
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Graphical_game_theory
Game theory dilemma
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Unscrupulous_diner's_dilemma
Game illustrating paradox in rational choice theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Dollar_auction
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
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
+ 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
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
Refinement of Nash equilibrium
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Sequential_equilibrium
Simple mathematical game
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Pirate_game
Concept in game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Markov_perfect_equilibrium
American economist (born 1948)
and Roberts suggested that this is why businesses had been unable to replicate Lincoln Electric's performance incentive system because the classic piece
Paul_Milgrom
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Symmetric_equilibrium
Aspect of game theory
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Self-confirming_equilibrium
Economic model
q_{2}}}=0.} The values of q 2 {\displaystyle q_{2}} that satisfy this equation are the best responses. Now the best response function of the leader is
Stackelberg_competition
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Glossary_of_game_theory
Zero-sum game where competitions between strategies contain a cycle
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Intransitive_game
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
Biological concept
stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Resource_holding_potential
REPLICATOR EQUATION
REPLICATOR EQUATION
Boy/Male
Tamil
Praroop | பà¯à®°à®¾à®°à¯‚பÂ
Replicate
Praroop | பà¯à®°à®¾à®°à¯‚பÂ
Boy/Male
Hindu, Indian
Replicate; Format
Boy/Male
Hindu
Replicate
REPLICATOR EQUATION
REPLICATOR EQUATION
REPLICATOR EQUATION
REPLICATOR EQUATION
REPLICATOR EQUATION
REPLICATOR EQUATION
REPLICATOR EQUATION
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.
v. t.
To reply.
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.
n.
The reply of the plaintiff, in matters of fact, to the defendant's plea.
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.
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.
a.
Alt. of Replicated
n.
The defendant's answer to the plaintiff's replication.
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 bringing of any term of an equation from one side over to the other without destroying the equation.
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.
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.
An identical equation.
n.
A repetition; a copy.
a.
Folded over or backward; folded back upon itself; as, a replicate leaf or petal; a replicate margin of a shell.
v. i.
To answer, as the defendant to the plaintiff's replication.
n.
Return or repercussion, as of sound; echo.
n.
An answer; a reply.
n.
One who unfolds or explains; an expounder; an explainer.