An evolutionarily stable strategy (ESS) is a
strategy
Strategy (from Greek στρατηγία ''stratēgia'', "art of troop leader; office of general, command, generalship") is a general plan to achieve one or more long-term or overall goals under conditions of uncertainty. In the sense of the "art ...
(or set of strategies) that is ''impermeable'' when adopted by a
population
Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...
in adaptation to a specific environment, that is to say it cannot be displaced by an alternative strategy (or set of strategies) which may be novel or initially rare. Introduced by
John Maynard Smith
John Maynard Smith (6 January 1920 – 19 April 2004) was a British theoretical and mathematical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics und ...
and
George R. Price
George Robert Price (October 6, 1922 – January 6, 1975) was an American population geneticist. Price is often noted for his formulation of the Price equation in 1967.
Originally a physical chemist and later a science journalist, he moved ...
in 1972/3,
it is an important concept in
behavioural ecology
Behavioral ecology, also spelled behavioural ecology, is the study of the evolutionary basis for animal behavior due to ecological pressures. Behavioral ecology emerged from ethology after Niko Tinbergen outlined four questions to address when ...
,
evolutionary psychology
Evolutionary psychology is a theoretical approach in psychology that examines cognition and behavior from a modern evolutionary perspective. It seeks to identify human psychological adaptations with regards to the ancestral problems they evolv ...
,
mathematical game theory and
economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and intera ...
, with applications in other fields such as
anthropology
Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, societies, and linguistics, in both the present and past, including past human species. Social anthropology studies patterns of behavi ...
,
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
and
political science
Political science is the scientific study of politics. It is a social science dealing with systems of governance and power, and the analysis of political activities, political thought, political behavior, and associated constitutions and la ...
.
In game-theoretical terms, an ESS is an
equilibrium refinement
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most com ...
of the
Nash equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equili ...
, being a Nash equilibrium that is also "evolutionarily
stable
A stable is a building in which livestock, especially horses, are kept. It most commonly means a building that is divided into separate stalls for individual animals and livestock. There are many different types of stables in use today; the ...
." Thus, once
fixed
Fixed may refer to:
* ''Fixed'' (EP), EP by Nine Inch Nails
* ''Fixed'', an upcoming 2D adult animated film directed by Genndy Tartakovsky
* Fixed (typeface), a collection of monospace bitmap fonts that is distributed with the X Window System
* ...
in a population,
natural selection
Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Charle ...
alone is sufficient to prevent alternative (
mutant
In biology, and especially in genetics, a mutant is an organism or a new genetic character arising or resulting from an instance of mutation, which is generally an alteration of the DNA sequence of the genome or chromosome of an organism. It ...
) strategies from replacing it (although this does not preclude the possibility that a better strategy, or set of strategies, will emerge in response to selective pressures resulting from environmental change).
History
Evolutionarily stable strategies were defined and introduced by
John Maynard Smith
John Maynard Smith (6 January 1920 – 19 April 2004) was a British theoretical and mathematical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics und ...
and
George R. Price
George Robert Price (October 6, 1922 – January 6, 1975) was an American population geneticist. Price is often noted for his formulation of the Price equation in 1967.
Originally a physical chemist and later a science journalist, he moved ...
in a 1973 ''
Nature
Nature, in the broadest sense, is the physics, physical world or universe. "Nature" can refer to the phenomenon, phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. ...
'' paper.
Such was the time taken in peer-reviewing the paper for ''Nature'' that this was preceded by a 1972 essay by Maynard Smith in a book of essays titled ''On Evolution''.
The 1972 essay is sometimes cited instead of the 1973 paper, but university libraries are much more likely to have copies of ''Nature''. Papers in ''Nature'' are usually short; in 1974, Maynard Smith published a longer paper in the ''
Journal of Theoretical Biology
The ''Journal of Theoretical Biology'' is a biweekly peer-reviewed scientific journal covering theoretical biology, as well as mathematical, computational, and statistical aspects of biology. Some research areas covered by the journal include cell ...
''. Maynard Smith explains further in his 1982 book ''
Evolution and the Theory of Games
''Evolution and the Theory of Games'' is a book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. The book was initially published in December 1982 by Cambridge University Press.
Overview
In the book, John Ma ...
''.
Sometimes these are cited instead. In fact, the ESS has become so central to game theory that often no citation is given, as the reader is assumed to be familiar with it.
Maynard Smith mathematically formalised a verbal argument made by Price, which he read while peer-reviewing Price's paper. When Maynard Smith realized that the somewhat disorganised Price was not ready to revise his article for publication, he offered to add Price as co-author.
The concept was derived from
R. H. MacArthur and
W. D. Hamilton
William Donald Hamilton (1 August 1936 – 7 March 2000) was a British evolutionary biologist, recognised as one of the most significant evolutionary theorists of the 20th century.
Hamilton became known for his theoretical work expounding a ...
's work on
sex ratio
The sex ratio (or gender ratio) is usually defined as the ratio of males to females in a population. As explained by Fisher's principle, for evolutionary reasons this is typically about 1:1 in species which reproduce sexually. Many species devia ...
s, derived from
Fisher's principle
Fisher's principle is an evolutionary model that explains why the sex ratio of most species that produce offspring through sexual reproduction is approximately 1:1 between males and females. A. W. F. Edwards has remarked that it is "probably the mo ...
, especially Hamilton's (1967) concept of an
unbeatable strategy
In biology, the idea of an unbeatable strategy was proposed by W.D. Hamilton in his 1967 paper on sex ratios in ''Science''. In this paper Hamilton discusses sex ratios as strategies in a game, and cites Verner as using this language in his 1965 ...
. Maynard Smith was jointly awarded the 1999
Crafoord Prize
The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord. The Prize is awarded in partnership between the Royal Swedish Academy of Sciences and the Crafoord Foun ...
for his development of the concept of evolutionarily stable strategies and the application of game theory to the evolution of behaviour.
Uses of ESS:
* The ESS was a major element used to analyze evolution in
Richard Dawkins
Richard Dawkins (born 26 March 1941) is a British evolutionary biologist and author. He is an emeritus fellow of New College, Oxford and was Professor for Public Understanding of Science in the University of Oxford from 1995 to 2008. An ath ...
' bestselling 1976 book ''
The Selfish Gene
''The Selfish Gene'' is a 1976 book on evolution by the ethologist Richard Dawkins, in which the author builds upon the principal theory of George C. Williams's ''Adaptation and Natural Selection'' (1966). Dawkins uses the term "selfish gene ...
''.
* The ESS was first used in the
social sciences
Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of soci ...
by
Robert Axelrod
Robert Marshall Axelrod (born May 27, 1943) is an American political scientist. He is Professor of Political Science and Public Policy at the University of Michigan where he has been since 1974. He is best known for his interdisciplinary work o ...
in his 1984 book ''
The Evolution of Cooperation
''The Evolution of Cooperation'' is a 1984 book written by political scientist Robert Axelrod that expands upon paper of the same name written by Axelrod and evolutionary biologist W.D. Hamilton. The book details a theory on the emergence of co ...
''. Since then, it has been widely used in the social sciences, including
anthropology
Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, societies, and linguistics, in both the present and past, including past human species. Social anthropology studies patterns of behavi ...
,
economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and intera ...
,
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
, and
political science
Political science is the scientific study of politics. It is a social science dealing with systems of governance and power, and the analysis of political activities, political thought, political behavior, and associated constitutions and la ...
.
* In the social sciences, the primary interest is not in an ESS as the end of
biological
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary in ...
evolution, but as an end point in
cultural evolution
Cultural evolution is an evolutionary theory of social change. It follows from the definition of culture as "information capable of affecting individuals' behavior that they acquire from other members of their species through teaching, imitation a ...
or individual learning.
* In
evolutionary psychology
Evolutionary psychology is a theoretical approach in psychology that examines cognition and behavior from a modern evolutionary perspective. It seeks to identify human psychological adaptations with regards to the ancestral problems they evolv ...
, ESS is used primarily as a model for
human biological evolution.
Motivation
The
Nash equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equili ...
is the traditional
solution concept
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most comm ...
in
game theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
. It depends on the cognitive abilities of the players. It is assumed that players are aware of the
structure of the game and consciously try to predict the
moves of their opponents and to maximize their own
payoffs. In addition, it is presumed that all the players know this (see
common knowledge
Common knowledge is knowledge that is publicly known by everyone or nearly everyone, usually with reference to the community in which the knowledge is referenced. Common knowledge can be about a broad range of subjects, such as science, literat ...
). These assumptions are then used to explain why players choose Nash equilibrium strategies.
Evolutionarily stable strategies are motivated entirely differently. Here, it is presumed that the players' strategies are biologically encoded and
heritable
Heredity, also called inheritance or biological inheritance, is the passing on of traits from parents to their offspring; either through asexual reproduction or sexual reproduction, the offspring cells or organisms acquire the genetic informa ...
. Individuals have no control over their strategy and need not be aware of the game. They reproduce and are subject to the forces of
natural selection
Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Charle ...
, with the payoffs of the game representing reproductive success (biological
fitness). It is imagined that alternative strategies of the game occasionally occur, via a process like
mutation
In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mi ...
. To be an ESS, a strategy must be resistant to these alternatives.
Given the radically different motivating assumptions, it may come as a surprise that ESSes and Nash equilibria often coincide. In fact, every ESS corresponds to a Nash equilibrium, but some Nash equilibria are not ESSes.
Nash equilibrium
An ESS is a
refined or modified form of a
Nash equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equili ...
. (See the next section for examples which contrast the two.) In a Nash equilibrium, if all players adopt their respective parts, no player can ''benefit'' by switching to any alternative strategy. In a two player game, it is a strategy pair. Let E(''S'',''T'') represent the payoff for playing strategy ''S'' against strategy ''T''. The strategy pair (''S'', ''S'') is a Nash equilibrium in a two player game if and only if for both players, for any strategy ''T'':
:E(''S'',''S'') ≥ E(''T'',''S'')
In this definition, a strategy ''T''≠''S'' can be a neutral alternative to ''S'' (scoring equally well, but not better).
A Nash equilibrium is presumed to be stable even if ''T'' scores equally, on the assumption that there is no long-term incentive for players to adopt ''T'' instead of ''S''. This fact represents the point of departure of the ESS.
Maynard Smith
John Maynard Smith (6 January 1920 – 19 April 2004) was a British theoretical and mathematical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics und ...
and
Price
A price is the (usually not negative) quantity of payment or compensation given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in the c ...
specify two conditions for a strategy ''S'' to be an ESS. For all ''T''≠''S'', either
# E(''S'',''S'') > E(''T'',''S''), or
# E(''S'',''S'') = E(''T'',''S'') and E(''S'',''T'') > E(''T'',''T'')
The first condition is sometimes called a ''strict'' Nash equilibrium. The second is sometimes called "Maynard Smith's second condition". The second condition means that although strategy ''T'' is neutral with respect to the payoff against strategy ''S'', the population of players who continue to play strategy ''S'' has an advantage when playing against ''T''.
There is also an alternative, stronger definition of ESS, due to Thomas.
This places a different emphasis on the role of the Nash equilibrium concept in the ESS concept. Following the terminology given in the first definition above, this definition requires that for all ''T''≠''S''
# E(''S'',''S'') ≥ E(''T'',''S''), and
# E(''S'',''T'') > E(''T'',''T'')
In this formulation, the first condition specifies that the strategy is a Nash equilibrium, and the second specifies that Maynard Smith's second condition is met. Note that the two definitions are not precisely equivalent: for example, each pure strategy in the coordination game below is an ESS by the first definition but not the second.
In words, this definition looks like this: The payoff of the first player when both players play strategy S is higher than (or equal to) the payoff of the first player when he changes to another strategy T and the second player keeps his strategy S ''and'' the payoff of the first player when only his opponent changes his strategy to T is higher than his payoff in case that both of players change their strategies to T.
This formulation more clearly highlights the role of the Nash equilibrium condition in the ESS. It also allows for a natural definition of related concepts such as a
weak ESS or an
evolutionarily stable set.
Examples of differences between Nash equilibria and ESSes
In most simple games, the ESSes and Nash equilibria coincide perfectly. For instance, in the
prisoner's dilemma
The Prisoner's Dilemma is an example of a game analyzed in game theory. It is also a thought experiment that challenges two completely rational agents to a dilemma: cooperate with their partner for mutual reward, or betray their partner ("defe ...
there is only one Nash equilibrium, and its strategy (''Defect'') is also an ESS.
Some games may have Nash equilibria that are not ESSes. For example, in harm thy neighbor (whose payoff matrix is shown here) both (''A'', ''A'') and (''B'', ''B'') are Nash equilibria, since players cannot do better by switching away from either. However, only ''B'' is an ESS (and a strong Nash). ''A'' is not an ESS, so ''B'' can neutrally invade a population of ''A'' strategists and predominate, because ''B'' scores higher against ''B'' than ''A'' does against ''B''. This dynamic is captured by Maynard Smith's second condition, since E(''A'', ''A'') = E(''B'', ''A''), but it is not the case that E(''A'',''B'') > E(''B'',''B'').
Nash equilibria with equally scoring alternatives can be ESSes. For example, in the game ''Harm everyone'', ''C'' is an ESS because it satisfies Maynard Smith's second condition. ''D'' strategists may temporarily invade a population of ''C'' strategists by scoring equally well against ''C'', but they pay a price when they begin to play against each other; ''C'' scores better against ''D'' than does ''D''. So here although E(''C'', ''C'') = E(''D'', ''C''), it is also the case that E(''C'',''D'') > E(''D'',''D''). As a result, ''C'' is an ESS.
Even if a game has pure strategy Nash equilibria, it might be that none of those pure strategies are ESS. Consider the
Game of chicken
The game of chicken, also known as the hawk–dove game or snowdrift game, is a model of conflict for two players in game theory. The principle of the game is that while the ideal outcome is for one player to yield (to avoid the worst outcome if ...
. There are two pure strategy Nash equilibria in this game (''Swerve'', ''Stay'') and (''Stay'', ''Swerve''). However, in the absence of an
uncorrelated asymmetry In game theory an uncorrelated asymmetry is an arbitrary asymmetry in a game which is otherwise symmetrical. The name 'uncorrelated asymmetry' is due to John Maynard Smith who called payoff relevant asymmetries in games with similar roles for each ...
, neither ''Swerve'' nor ''Stay'' are ESSes. There is a third Nash equilibrium, a
mixed strategy
In game theory, a player's strategy is any of the options which they choose in a setting where the outcome depends ''not only'' on their own actions ''but'' on the actions of others. The discipline mainly concerns the action of a player in a game ...
which is an ESS for this game (see
Hawk-dove game
The game of chicken, also known as the hawk–dove game or snowdrift game, is a model of conflict for two players in game theory. The principle of the game is that while the ideal outcome is for one player to yield (to avoid the worst outcome if ...
and
Best response
In game theory, the best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given (; ). The concept of a best response is central to John Nash's best-known contribu ...
for explanation).
This last example points to an important difference between Nash equilibria and ESS. Nash equilibria are defined on ''strategy sets'' (a specification of a strategy for each player), while ESS are defined in terms of strategies themselves. The equilibria defined by ESS must always be
symmetric
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
, and thus have fewer equilibrium points.
Vs. evolutionarily stable state
In population biology, the two concepts of an ''evolutionarily stable strategy'' (ESS) and an ''
evolutionarily stable state A population can be described as being in an evolutionarily stable state when that population's "genetic composition is restored by selection after a disturbance, provided the disturbance is not too large" (Maynard Smith, 1982).Maynard Smith, J.. (1 ...
'' are closely linked but describe different situations.
In an evolutionarily stable ''strategy,'' if all the members of a population adopt it, no mutant strategy can invade.
Once virtually all members of the population use this strategy, there is no 'rational' alternative. ESS is part of classical
game theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
.
In an evolutionarily stable ''state,'' a population's genetic composition is restored by selection after a disturbance, if the disturbance is not too large. An evolutionarily stable state is a dynamic property of a population that returns to using a strategy, or mix of strategies, if it is perturbed from that initial state. It is part of
population genetics
Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and pop ...
,
dynamical system
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...
, or
evolutionary game theory
Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Ma ...
. This is now called convergent stability.
B. Thomas (1984) applies the term ESS to an individual strategy which may be mixed, and evolutionarily stable population state to a population mixture of pure strategies which may be formally equivalent to the mixed ESS.
Whether a population is evolutionarily stable does not relate to its genetic diversity: it can be genetically monomorphic or
polymorphic.
Stochastic ESS
In the classic definition of an ESS, no mutant strategy can invade. In finite populations, any mutant could in principle invade, albeit at low probability, implying that no ESS can exist. In an infinite population, an ESS can instead be defined as a strategy which, should it become invaded by a new mutant strategy with probability p, would be able to counterinvade from a single starting individual with probability >p, as illustrated by the evolution of
bet-hedging.
Prisoner's dilemma
A common model of
altruism
Altruism is the principle and moral practice of concern for the welfare and/or happiness of other human beings or animals, resulting in a quality of life both material and spiritual. It is a traditional virtue in many cultures and a core as ...
and social cooperation is the
Prisoner's dilemma
The Prisoner's Dilemma is an example of a game analyzed in game theory. It is also a thought experiment that challenges two completely rational agents to a dilemma: cooperate with their partner for mutual reward, or betray their partner ("defe ...
. Here a group of players would collectively be better off if they could play ''Cooperate'', but since ''Defect'' fares better each individual player has an incentive to play ''Defect''. One solution to this problem is to introduce the possibility of retaliation by having individuals play the game repeatedly against the same player. In the so-called ''
iterated'' Prisoner's dilemma, the same two individuals play the prisoner's dilemma over and over. While the Prisoner's dilemma has only two strategies (''Cooperate'' and ''Defect''), the iterated Prisoner's dilemma has a huge number of possible strategies. Since an individual can have different contingency plan for each history and the game may be repeated an indefinite number of times, there may in fact be an infinite number of such contingency plans.
Three simple contingency plans which have received substantial attention are ''Always Defect'', ''Always Cooperate'', and ''
Tit for Tat
Tit for tat is an English saying meaning "equivalent retaliation". It developed from "tip for tap", first recorded in 1558.
It is also a highly effective strategy in game theory. An agent using this strategy will first cooperate, then subseque ...
''. The first two strategies do the same thing regardless of the other player's actions, while the latter responds on the next round by doing what was done to it on the previous round—it responds to ''Cooperate'' with ''Cooperate'' and ''Defect'' with ''Defect''.
If the entire population plays ''Tit-for-Tat'' and a mutant arises who plays ''Always Defect'', ''Tit-for-Tat'' will outperform ''Always Defect''. If the population of the mutant becomes too large — the percentage of the mutant will be kept small. ''Tit for Tat'' is therefore an ESS, ''with respect to only these two strategies''. On the other hand, an island of ''Always Defect'' players will be stable against the invasion of a few ''Tit-for-Tat'' players, but not against a large number of them. If we introduce ''Always Cooperate'', a population of ''Tit-for-Tat'' is no longer an ESS. Since a population of ''Tit-for-Tat'' players always cooperates, the strategy ''Always Cooperate'' behaves identically in this population. As a result, a mutant who plays ''Always Cooperate'' will not be eliminated. However, even though a population of ''Always Cooperate'' and ''Tit-for-Tat'' can coexist, if there is a small percentage of the population that is ''Always Defect'', the selective pressure is against ''Always Cooperate'', and in favour of ''Tit-for-Tat''. This is due to the lower payoffs of cooperating than those of defecting in case the opponent defects.
This demonstrates the difficulties in applying the formal definition of an ESS to games with large strategy spaces, and has motivated some to consider alternatives.
Human behavior
The fields of
sociobiology
Sociobiology is a field of biology that aims to examine and explain social behavior in terms of evolution. It draws from disciplines including psychology, ethology, anthropology, evolution, zoology, archaeology, and population genetics. Within t ...
and
evolutionary psychology
Evolutionary psychology is a theoretical approach in psychology that examines cognition and behavior from a modern evolutionary perspective. It seeks to identify human psychological adaptations with regards to the ancestral problems they evolv ...
attempt to explain animal and human behavior and social structures, largely in terms of evolutionarily stable strategies.
Sociopathy
Psychopathy, sometimes considered synonymous with sociopathy, is characterized by persistent antisocial behavior, impaired empathy and remorse, and bold, disinhibited, and egotistical traits. Different conceptions of psychopathy have been u ...
(chronic antisocial or criminal behavior) may be a result of a combination of two such strategies.
Evolutionarily stable strategies were originally considered for biological evolution, but they can apply to other contexts. In fact, there are stable states for a large class of
adaptive dynamics
Evolutionary invasion analysis, also known as adaptive dynamics, is a set of mathematical modeling techniques that use differential equations to study the long-term evolution of Phenotypic trait, traits in Asexual reproduction, asexually reprodu ...
. As a result, they can be used to explain human behaviours that lack any genetic influences.
See also
*
Antipredator adaptation
Anti-predator adaptations are mechanisms developed through evolution that assist prey organisms in their constant struggle against predators. Throughout the animal kingdom, adaptations have evolved for every stage of this struggle, namely by avo ...
*
Behavioral ecology
Behavioral ecology, also spelled behavioural ecology, is the study of the evolutionary basis for animal behavior due to ecological pressures. Behavioral ecology emerged from ethology after Niko Tinbergen outlined four questions to address when ...
*
Evolutionary psychology
Evolutionary psychology is a theoretical approach in psychology that examines cognition and behavior from a modern evolutionary perspective. It seeks to identify human psychological adaptations with regards to the ancestral problems they evolv ...
*
Fitness landscape
Fitness may refer to:
* Physical fitness, a state of health and well-being of the body
* Fitness (biology), an individual's ability to propagate its genes
* Fitness (cereal), a brand of breakfast cereals and granola bars
* ''Fitness'' (magazine), ...
*
Hawk–dove game
*
Koinophilia
Koinophilia is an evolutionary hypothesis proposing that during sexual selection, animals preferentially seek mates with a minimum of unusual or mutant features, including functionality, appearance and behavior. Koinophilia intends to explain th ...
*
Sociobiology
Sociobiology is a field of biology that aims to examine and explain social behavior in terms of evolution. It draws from disciplines including psychology, ethology, anthropology, evolution, zoology, archaeology, and population genetics. Within t ...
*
War of attrition (game)
In game theory, the ''war of attrition'' is a dynamic timing game in which players choose a time to stop, and fundamentally trade off the strategic gains from outlasting other players and the real costs expended with the passage of time. Its preci ...
References
Further reading
* Classic reference textbook.
*
* . An 88-page mathematical introduction; see Section 3.8
Free onlineat many universities.
*
Parker, G. A. (1984) Evolutionary stable strategies. In ''Behavioural Ecology: an Evolutionary Approach'' (2nd ed)
Krebs, J. R. & Davies N.B., eds. pp 30–61. Blackwell, Oxford.
* . A comprehensive reference from a computational perspective; see Section 7.7
Downloadable free online
*
Maynard Smith, John. (1982) ''
Evolution and the Theory of Games
''Evolution and the Theory of Games'' is a book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. The book was initially published in December 1982 by Cambridge University Press.
Overview
In the book, John Ma ...
''. . Classic reference.
External links
Evolutionarily Stable Strategiesat Animal Behavior: An Online Textbook by Michael D. Breed.
Kenneth N. Prestwich's site at College of the Holy Cross.
Evolutionarily stable strategies knol
{{DEFAULTSORT:Evolutionarily Stable Strategy
Game theory equilibrium concepts
Evolutionary game theory