Complete Mixing

In evolutionary game theory, complete mixing refers to an assumption about the type of interactions that occur between individual organisms. Interactions between individuals in a population attains complete mixing if and only if the probably individual x interacts with individual y is equal for all y.

This assumption is implicit in the replicator equation a system of differential equations that represents one model in evolutionary game theory. This assumption usually does not hold for most organismic populations, since usually interactions occur in some spatial setting where individuals are more likely to interact with those around them. Although the assumption is empirically violated, it represents a certain sort of scientific idealization which may or may not be harmful to the conclusions reached by that model. This question has led individuals to investigate a series of other models where there is not complete mixing (e.g. Cellular automata models).

Topics in population genetics

Key concepts	Hardy-Weinberg law Genetic linkage Linkage disequilibrium Fisher's fundamental theorem Neutral theory Price equation

Selection	Natural Sexual Artificial Ecological

Effects of selection on genomic variation	Genetic hitchhiking Background selection

Genetic drift	Small population size Population bottleneck Founder effect Coalescence Balding–Nichols model

Founders	R. A. Fisher J. B. S. Haldane Sewall Wright

Related topics	Evolution Microevolution Evolutionary game theory Fitness landscape Genetic genealogy

List of evolutionary biology topics

Topics in game theory

Definitions	Normal-form game Extensive-form game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian-Nash Perfect Bayesian Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Cheap talk Zero–sum game Mechanism design Bargaining problem Stochastic game Large poisson game Nontransitive game Global games

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Cake cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Screening game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key Figures	Kenneth Arrow Robert Aumann Kenneth Binmore Samuel Bowles Melvin Dresher Merrill M. Flood Drew Fudenberg Donald B. Gillies John Harsanyi Leonid Hurwicz David K. Levine Daniel Kahneman Harold W. Kuhn Eric Maskin Jean-François Mertens Paul Milgrom Oskar Morgenstern Roger Myerson John Nash John von Neumann Ariel Rubinstein Thomas Schelling Reinhard Selten Herbert Simon Lloyd Shapley John Maynard Smith Jean Tirole Albert W. Tucker William Vickrey Robert B. Wilson Peyton Young

See also	Tragedy of the commons Tyranny of small decisions All-pay auction List of games in game theory Confrontation Analysis

Famous quotes containing the words complete and/or mixing:

“For us to go to Italy and to penetrate into Italy is like a most fascinating act of self-discovery—back, back down the old ways of time. Strange and wonderful chords awake in us, and vibrate again after many hundreds of years of complete forgetfulness.”
—D.H. (David Herbert)

“How natural that the errors of the ancient should be handed down and, mixing with the principles and system which Christ taught, give to us an adulterated Christianity.”
—Olympia Brown (1835–1900)