Memetics

From Wikipedia, the free encyclopedia

Memetics is the study of information and culture based on an analogy with Darwinian evolution. Proponents describe memetics as an approach to evolutionary models of cultural information transfer. Critics regard memetics as a pseudoscience.^{[citation needed]} Memetics describes how an idea can propogate successfully, but doesn't necessarily imply a concept is factual.^[1]

The term meme was coined in Richard Dawkins' 1976 book The Selfish Gene, but Dawkins later distanced himself from the resulting field of study.^[2] Analogous to a gene, the meme was conceived as a "unit of culture" (an idea, belief, pattern of behaviour, etc.) which is "hosted" in the minds of one or more individuals, and which can reproduce itself in the sense of jumping from the mind of one person to the mind of another. Thus what would otherwise be regarded as one individual influencing another to adopt a belief is seen as an idea-replicator reproducing itself in a new host. As with genetics, particularly under a Dawkinsian interpretation, a meme's success may be due to its contribution to the effectiveness of its host.

The Usenet newsgroup alt.memetics started in 1993 with peak posting years in the mid to late 1990s.^[3] The Journal of Memetics was published electronically from 1997 to 2005.^[4]

History

In his book The Selfish Gene (1976), the evolutionary biologist Richard Dawkins used the term meme to describe a unit of human cultural transmission analogous to the gene, arguing that replication also happens in culture, albeit in a different sense. Bella Hiscock outlined a similar hypothesis in 1975,^[5] which Dawkins referenced. Cultural evolution itself is a much older topic, with a history that dates back at least as far as Darwin's era.

Dawkins (1976) proposed that the meme is a unit of information residing in the brain and is the mutating replicator in human cultural evolution. It is a pattern that can influence its surroundings – that is, it has causal agency – and can propagate. This proposal resulted in debate among sociologists, biologists, and scientists of other disciplines. Dawkins himself did not provide a sufficient explanation of how the replication of units of information in the brain controls human behaviour and ultimately culture, and the principal topic of the book was genetics. Dawkins apparently did not intend to present a comprehensive theory of memetics in The Selfish Gene, but rather coined the term meme in a speculative spirit. Accordingly, different researchers came to define the term "unit of information" in different ways.

The modern memetics movement dates from the mid-1980s. A January 1983 "Metamagical Themas" column^[6] by Douglas Hofstadter, in Scientific American, was influential – as was his 1985 book of the same name. "Memeticist" was coined as analogous to "geneticist" – originally in The Selfish Gene. Later Arel Lucas suggested that the discipline that studies memes and their connections to human and other carriers of them be known as "memetics" by analogy with "genetics".^[7] Dawkins' The Selfish Gene has been a factor in attracting the attention of people of disparate intellectual backgrounds. Another stimulus was the publication in 1991 of Consciousness Explained by Tufts University philosopher Daniel Dennett, which incorporated the meme concept into a theory of the mind. In his 1991 essay "Viruses of the Mind", Richard Dawkins used memetics to explain the phenomenon of religious belief and the various characteristics of organised religions. By then, memetics had also become a theme appearing in fiction (e.g. Neal Stephenson's Snow Crash).

The idea of language as a virus had already been introduced by William S. Burroughs as early as 1962 in his book The Ticket That Exploded, and later in The Electronic Revolution, published in 1970 in The Job. Douglas Rushkoff explored the same concept in Media Virus: Hidden Agendas in Popular Culture in 1995.

However, the foundation of memetics in its full modern incarnation originated in the publication in 1996 of two books by authors outside the academic mainstream: Virus of the Mind: The New Science of the Meme by former Microsoft executive turned motivational speaker and professional poker-player, Richard Brodie, and Thought Contagion: How Belief Spreads Through Society by Aaron Lynch, a mathematician and philosopher who worked for many years as an engineer at Fermilab. Lynch claimed to have conceived his theory totally independently of any contact with academics in the cultural evolutionary sphere, and apparently was not even aware of Dawkins' The Selfish Gene until his book was very close to publication.

Around the same time as the publication of the books by Lynch and Brodie the e-journal Journal of Memetics – Evolutionary Models of Information Transmission appeared on the web. It was first hosted by the Centre for Policy Modelling at Manchester Metropolitan University but later taken over by Francis Heylighen of the CLEA research institute at the Vrije Universiteit Brussel. The e-journal soon became the central point for publication and debate within the nascent memeticist community. (There had been a short-lived paper-based memetics publication starting in 1990, the Journal of Ideas edited by Elan Moritz.^[8]) In 1999, Susan Blackmore, a psychologist at the University of the West of England, published The Meme Machine, which more fully worked out the ideas of Dennett, Lynch, and Brodie and attempted to compare and contrast them with various approaches from the cultural evolutionary mainstream, as well as providing novel, and controversial, memetics-based theories for the evolution of language and the human sense of individual selfhood.

The term "meme"

The term "meme" derives from the Ancient Greek μιμητής (mimētḗs), meaning "imitator, pretender". The similar term "mneme" was used in 1904, by the German evolutionary biologist Richard Semon, best known for his development of the engram theory of memory, in his work Die mnemischen Empfindungen in ihren Beziehungen zu den Originalempfindungen, translated into English in 1921 as The Mneme^{[citation needed]}. Until Daniel Schacter published Forgotten Ideas, Neglected Pioneers: Richard Semon and the Story of Memory in 2000, Semon's work had little influence, though it was quoted extensively in Erwin Schrödinger’s prescient 1956 Tarner Lecture “Mind and Matter”. Richard Dawkins (1976) apparently coined the word "meme" independently of Semon, writing this:

"'Mimeme' comes from a suitable Greek root, but I want a monosyllable that sounds a bit like 'gene'. I hope my classicist friends will forgive me if I abbreviate mimeme to meme. If it is any consolation, it could alternatively be thought of as being related to 'memory', or to the French word même."^{[citation needed]}

Maturity

In 2005, the Journal of Memetics – Evolutionary Models of Information Transmission ceased publication and published a set of articles on the future of memetics. The website states that although "there was to be a relaunch...after several years nothing has happened".^[9] Susan Blackmore has left the University of the West of England to become a freelance science-writer and now concentrates more on the field of consciousness and cognitive science. Derek Gatherer moved to work as a computer programmer in the pharmaceutical industry, although he still occasionally publishes on memetics-related matters. Richard Brodie is now climbing the world professional poker rankings. Aaron Lynch disowned the memetics community and the words "meme" and "memetics" (without disowning the ideas in his book), adopting the self-description "thought contagionist". He died in 2005.

Susan Blackmore (2002) re-stated the definition of meme as: whatever is copied from one person to another person, whether habits, skills, songs, stories, or any other kind of information. Further she said that memes, like genes, are replicators in the sense as defined by Dawkins.^[10] That is, they are information that is copied. Memes are copied by imitation, teaching and other methods. The copies are not perfect: memes are copied with variation; moreover, they compete for space in our memories and for the chance to be copied again. Only some of the variants can survive. The combination of these three elements (copies; variation; competition for survival) forms precisely the condition for Darwinian evolution, and so memes (and hence human cultures) evolve. Large groups of memes that are copied and passed on together are called co-adapted meme complexes, or memeplexes. In Blackmore's definition, the way that a meme replicates is through imitation. This requires brain capacity to generally imitate a model or selectively imitate the model. Since the process of social learning varies from one person to another, the imitation process cannot be said to be completely imitated. The sameness of an idea may be expressed with different memes supporting it. This is to say that the mutation rate in memetic evolution is extremely high, and mutations are even possible within each and every iteration of the imitation process. It becomes very interesting when we see that a social system composed of a complex network of microinteractions exists, but at the macro level an order emerges to create culture.^{[citation needed]}

Internalists and externalists

The memetics movement split almost immediately into two. The first group were those who wanted to stick to Dawkins' definition of a meme as "a unit of cultural transmission". Gibron Burchett, another memeticist responsible for helping to research and co-coin the term memetic engineering, along with Leveious Rolando and Larry Lottman, has stated that a meme can be defined, more precisely, as "a unit of cultural information that can be copied, located in the brain". This thinking is more in line with Dawkins' second definition of the meme in his book The Extended Phenotype. The second group wants to redefine memes as observable cultural artifacts and behaviors. However, in contrast to those two positions, Blackmore does not reject either concept of external or internal memes.^[11]

These two schools became known as the "internalists" and the "externalists." Prominent internalists included both Lynch and Brodie; the most vocal externalists included Derek Gatherer, a geneticist from Liverpool John Moores University, and William Benzon, a writer on cultural evolution and music. The main rationale for externalism was that internal brain entities are not observable, and memetics cannot advance as a science, especially a quantitative science, unless it moves its emphasis onto the directly quantifiable aspects of culture. Internalists countered with various arguments: that brain states will eventually be directly observable with advanced technology, that most cultural anthropologists agree that culture is about beliefs and not artifacts, or that artifacts cannot be replicators in the same sense as mental entities (or DNA) are replicators. The debate became so heated that a 1998 Symposium on Memetics, organised as part of the 15th International Conference on Cybernetics, passed a motion calling for an end to definitional debates. McNamara demonstrated in 2011 that functional connectivity profiling using neuroimaging tools enables the observation of the processing of internal memes, "i-memes", in response to external "e-memes".^[12]

An advanced statement of the internalist school came in 2002 with the publication of The Electric Meme, by Robert Aunger, an anthropologist from the University of Cambridge. Aunger also organised a conference in Cambridge in 1999, at which prominent sociologists and anthropologists were able to give their assessment of the progress made in memetics to that date. This resulted in the publication of Darwinizing Culture: The Status of Memetics as a Science, edited by Aunger and with a foreword by Dennett, in 2001^[13].

Criticism

This evolutionary model of cultural information transfer is based on the concept that units of information, or "memes", have an independent existence, are self-replicating, and are subject to selective evolution through environmental forces.^[14] Starting from a proposition put forward in the writings of Richard Dawkins, this model has formed the basis of a new area of study, one that looks at the self-replicating units of culture. It has been proposed that just as memes are analogous to genes, memetics is analogous to genetics.

Critics contend that some proponents' assertions are "untested, unsupported or incorrect."^[14] Luis Benitez-Bribiesca, a critic of memetics, calls it "a pseudoscientific dogma" and "a dangerous idea that poses a threat to the serious study of consciousness and cultural evolution" among other things. As factual criticism, he refers to the lack of a code script for memes, as the DNA is for genes, and to the fact that the meme mutation mechanism (i.e., an idea going from one brain to another) is too unstable (low replication accuracy and high mutation rate), which would render the evolutionary process chaotic.^[15] This, however, has been demonstrated (e.g. by Daniel C. Dennett, in Darwin's Dangerous Idea) to not be the case, in fact, due to the existence of self-regulating correction mechanisms (vaguely resembling those of gene transcription) enabled by the redundancy and other properties of most meme expression languages, which do stabilize information transfer. (E.g. spiritual narratives—including music and dance forms—can survive in full detail across any number of generations even in cultures with oral tradition only.) Memes for which stable copying methods are available will inevitably get selected for survival more often than those which can only have unstable mutations, therefore going extinct. (Notably, Benitez-Bribiesca's claim of "no code script" is also irrelevant, considering the fact that there is nothing preventing the information contents of memes from being coded, encoded, expressed, preserved or copied in all sorts of different ways throughout their life-cycles.)

Another criticism comes from semiotics, (e.g., Deacon,^[16] Kull^[17]) stating that the concept of meme is a primitivized concept of Sign. Meme is thus described in memetics as a sign without its triadic nature. In other words, meme is a degenerate sign, which includes only its ability of being copied. Accordingly, in the broadest sense, the objects of copying are memes, whereas the objects of translation and interpretation are signs.

Mary Midgley criticises memetics for at least two reasons:^[18] "One, culture is not best understood by examining its smallest parts, as culture is pattern-like, comparable to an ocean current. Many more factors, historical and others, should be taken into account than only whatever particle culture is built from. Two, if memes are not thoughts (and thus not cognitive phenomena), as Daniel C. Dennett insists in "Darwin's Dangerous Idea", then their ontological status is open to question, and memeticists (who are also reductionists) may be challenged whether memes even exist. Questions can extend to whether the idea of "meme" is itself a meme, or is a true concept. Fundamentally, memetics is an attempt to produce knowledge through organic metaphors, which as such is a questionable research approach, as the application of metaphors has the effect of hiding that which does not fit within the realm of the metaphor. Rather than study actual reality, without preconceptions, memetics, as so many of the socio-biological explanations of society, believe that saying that the apple is like an orange is a valid analysis of the apple."^[19]

Henry Jenkins, Joshua Green, and Sam Ford, in their book Spreadable Media (2013), criticize Dawkins' idea of the meme, writing that "while the idea of the meme is a compelling one, it may not adequately account for how content circulates through participatory culture." The three authors also criticize other interpretations of memetics, especially those which describe memes as "self-replicating", because they ignore the fact that "culture is a human product and replicates through human agency."^[20]

Like other critics, Maria Kronfeldner has criticized memetics for being based on an allegedly inaccurate analogy with the gene; alternately, she claims it is "heuristically trivial", being a mere redescription of what is already known without offering any useful novelty.^[21]

New developments

Dawkins in A Devil's Chaplain responded that there are actually two different types of memetic processes (controversial and informative). The first is a type of cultural idea, action, or expression, which does have high variance; for instance, a student of his who had inherited some of the mannerisms of Wittgenstein. However, he also describes a self-correcting meme, highly resistant to mutation. As an example of this, he gives origami patterns in elementary schools – except in rare cases, the meme is either passed on in the exact sequence of instructions, or (in the case of a forgetful child) terminates. This type of meme tends not to evolve, and to experience profound mutations in the rare event that it does.

Another definition, given by Hokky Situngkir, tried to offer a more rigorous formalism for the meme, memeplexes, and the deme, seeing the meme as a cultural unit in a cultural complex system. It is based on the Darwinian genetic algorithm with some modifications to account for the different patterns of evolution seen in genes and memes. In the method of memetics as the way to see culture as a complex adaptive system,^[22] he describes a way to see memetics as an alternative methodology of cultural evolution. However, there are as many possible definitions that are credited to the word "meme". For example, in the sense of computer simulation the term memetic algorithm is used to define a particular computational viewpoint.

The possibility of quantitative analysis of memes using neuroimaging tools and the suggestion that such studies have already been done was given by McNamara (2011).^[23] This author proposes hyperscanning (concurrent scanning of two communicating individuals in two separate MRI machines) as a key tool in the future for investigating memetics.

Velikovsky (2013) proposed the "holon" as the structure of the meme,^[24] synthesizing the major theories on memes of Richard Dawkins, Mihaly Csikszentmihalyi, E. O. Wilson, Frederick Turner (poet) and Arthur Koestler.^{[clarification needed]}

Proponents of memetics as described in the Journal of Memetics (out of print since 2005^[25] ) – Evolutionary Models of Information Transmission believe that 'memetics' has the potential to be an important and promising analysis of culture using the framework of evolutionary concepts. Keith Henson in Memetics and the Modular-Mind (Analog Aug. 1987)^[26] makes the case that memetics needs to incorporate evolutionary psychology to understand the psychological traits of a meme's host.^[27] This is especially true of time-varying, meme-amplification host-traits, such as those leading to wars.^[28][29]

DiCarlo (^{[year needed]}) has developed the idea of 'memetic equilibrium' to describe a cultural compatible state with biological equilibrium. In "Problem Solving and Neurotransmission in the Upper Paleolithic" (in press^{[clarification needed]}), diCarlo argues that as human consciousness evolved and developed, so too did our ancestors' capacity to consider and attempt to solve environmental problems in more conceptually sophisticated ways. Understood in this way, problem solving amongst a particular group, when considered satisfactory, often produces a feeling of environmental control, stability, in short—memetic equilibrium. But the pay-off is not merely practical, providing purely functional utility—it is biochemical and it comes in the form of neurotransmitters. The relationship between a gradually emerging conscious awareness and sophisticated languages in which to formulate representations combined with the desire to maintain biological equilibrium, generated the necessity for equilibrium to fill in conceptual gaps in terms of understanding three very important aspects in the Upper Paleolithic: causality, morality, and mortality. The desire to explain phenomena in relation to maintaining survival and reproductive stasis, generated a normative stance in the minds of our ancestors—Survival/Reproductive Value (or S-R Value).

Houben (2014) has argued on several occasions that the exceptional resilience of Vedic ritual and its interaction with a changing ecological and economic environment over several millennia can be profitably dealt with in a ‘cultural evolution’ perspective in which the Vedic mantra is the ‘meme’ or unit of cultural replication.^[30] This renders superfluous attempts^{[by whom?]} to explain the phenomenon of Vedic tradition in genetic^{[clarification needed]} terms.^[31] The domain of Vedic ritual should be able^{[clarification needed]} to fulfil to a large extent the three challenges posed to memetics by B. Edmonds (2002 and 2005).^[32]

Applications

Research methodologies that apply memetics go by many names: Viral marketing, cultural evolution, the history of ideas, social analytics, and more. Many of these applications do not make reference to the literature on memes directly but are built upon the evolutionary lens of idea propagation that treats semantic units of culture as self-replicating and mutating patterns of information that are assumed to be relevant for scientific study. For example, the field of public relations is filled with attempts to introduce new ideas and alter social discourse. One means of doing this is to design a meme and deploy it through various media channels. One historic example of applied memetics is the PR campaign conducted in 1991 as part of the build-up to the first Gulf War in the United States.^[33]

The application of memetics to a difficult complex social system problem, environmental sustainability, has recently been attempted at thwink.org^[34] Using meme types and memetic infection in several stock and flow simulation models, Jack Harich has demonstrated several interesting phenomena that are best, and perhaps only, explained by memes. One model, The Dueling Loops of the Political Powerplace,^[35] argues that the fundamental reason corruption is the norm in politics is due to an inherent structural advantage of one feedback loop pitted against another. Another model, The Memetic Evolution of Solutions to Difficult Problems,^[36] uses memes, the evolutionary algorithm, and the scientific method to show how complex solutions evolve over time and how that process can be improved. The insights gained from these models are being used to engineer memetic solution elements to the sustainability problem.

Another application of memetics in the sustainability space is the crowdfunded Climate Meme Project^[37] conducted by Joe Brewer and Balazs Laszlo Karafiath in the spring of 2013. This study was based on a collection of 1000 unique text-based expressions gathered from Twitter, Facebook, and structured interviews with climate activists. The major finding was that the global warming meme is not effective at spreading because it causes emotional duress in the minds of people who learn about it. Five central tensions were revealed in the discourse about [climate change], each of which represents a resonance point through which dialogue can be engaged. The tensions were Harmony/Disharmony (whether or not humans are part of the natural world), Survival/Extinction (envisioning the future as either apocalyptic collapse of civilization or total extinction of the human race), Cooperation/Conflict (regarding whether or not humanity can come together to solve global problems), Momentum/Hesitation (about whether or not we are making progress at the collective scale to address climate change), and Elitism/Heretic (a general sentiment that each side of the debate considers the experts of its opposition to be untrustworthy).^[38]

Ben Cullen, in his book Contagious Ideas,^[39] brought the idea of the meme into the discipline of archaeology. He coined the term "Cultural Virus Theory", and used it to try to anchor archaeological theory in a neo-Darwinian paradigm. Archaeological memetics could assist the application of the meme concept to material culture in particular.

Francis Heylighen of the Center Leo Apostel for Interdisciplinary Studies has postulated what he calls "memetic selection criteria". These criteria opened the way to a specialized field of applied memetics to find out if these selection criteria could stand the test of quantitative analyses. In 2003 Klaas Chielens carried out these tests in a Masters thesis project on the testability of the selection criteria.

In Selfish Sounds and Linguistic Evolution,^[40] Austrian linguist Nikolaus Ritt has attempted to operationalise memetic concepts and use them for the explanation of long term sound changes and change conspiracies in early English. It is argued that a generalised Darwinian framework for handling cultural change can provide explanations where established, speaker centred approaches fail to do so. The book makes comparatively concrete suggestions about the possible material structure of memes, and provides two empirically rich case studies.

Australian academic S.J. Whitty has argued that project management is a memeplex with the language and stories of its practitioners at its core.^[41] This radical approach sees a project and its management as an illusion; a human construct about a collection of feelings, expectations, and sensations, which are created, fashioned, and labeled by the human brain. Whitty's approach requires project managers to consider that the reasons for using project management are not consciously driven to maximize profit, and are encouraged to consider project management as naturally occurring, self-serving, evolving process which shapes organizations for its own purpose.

Swedish political scientist Mikael Sandberg argues against "Lamarckian" interpretations of institutional and technological evolution and studies creative innovation of information technologies in governmental and private organizations in Sweden in the 1990s from a memetic perspective.^[42] Comparing the effects of active ("Lamarckian") IT strategy versus user–producer interactivity (Darwinian co-evolution), evidence from Swedish organizations shows that co-evolutionary interactivity is almost four times as strong a factor behind IT creativity as the "Lamarckian" IT strategy.

Terminology

• Memeplex – (an abbreviation of meme-complex) is a collection or grouping of memes that have evolved into a mutually supportive or symbiotic relationship.^[43] Simply put, a meme-complex is a set of ideas that reinforce each other. Meme-complexes are roughly analogous to the symbiotic collection of individual genes that make up the genetic codes of biological organisms. An example of a memeplex would be a religion.
• Meme pool – a population of interbreeding memes.
• Memetic engineering – The process of deliberately creating memes, using engineering principles.
• Memetic algorithms – an approach to evolutionary computation that attempts to emulate cultural evolution in order to solve optimization problems.
• Memotype – is the actual information-content of a meme.^[44]
• Memeoid – is a neologism for people who have been taken over by a meme to the extent that their own survival becomes inconsequential. Examples include kamikazes, suicide bombers and cult members who commit mass suicide. The term was apparently coined by H. Keith Henson in "Memes, L5 and the Religion of the Space Colonies," L5 News, September 1985 pp. 5–8,^[45] and referenced in the expanded second edition of Richard Dawkins' book The Selfish Gene (p. 330). But in the strict sense all people are essentially memeoid, since no distinction can be made if one uses language, or memes use their host. In The Electronic Revolution William S. Burroughs writes: "the word has not been recognised as a virus because it has achieved a state of stable symbiosis with the host."
• Memetic equilibrium – refers to the cultural equivalent of species biological equilibrium. It is that which humans strive for in terms of personal value with respect to cultural artefacts and ideas. The term was coined by Christopher diCarlo.^[46]

Evolutionary game theory

From Wikipedia, the free encyclopedia

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 Maynard Smith and George R. Price's formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies.^[1]

Evolutionary game theory differs from classical game theory in focusing more on the dynamics of strategy change. This is influenced by the frequency of the competing strategies in the population.^[2]

Evolutionary game theory has helped to explain the basis of altruistic behaviours in Darwinian evolution. It has in turn become of interest to economists, sociologists, anthropologists, and philosophers.

History

Classical game theory

Classical non-cooperative game theory was conceived by John von Neumann to determine optimal strategies in competitions between adversaries. A contest involves players, all of whom have a choice of moves. Games can be a single round or repetitive. The approach a player takes in making his moves constitutes his strategy. Rules govern the outcome for the moves taken by the players, and outcomes produce payoffs for the players; rules and resulting payoffs can be expressed as decision trees or in a payoff matrix. Classical theory requires the players to make rational choices. Each player must consider the strategic analysis that his opponents are making to make his own choice of moves.^[3][4]

The problem of ritualized behaviour

The mathematical biologist John Maynard Smith modelled evolutionary games.

Evolutionary game theory started with the problem of how to explain ritualized animal behaviour in a conflict situation; "why are animals so 'gentlemanly or ladylike' in contests for resources?" The leading ethologists Niko Tinbergen and Konrad Lorenz proposed that such behaviour exists for the benefit of the species. John Maynard Smith considered that incompatible with Darwinian thought,^[5] where selection occurs at an individual level, so self-interest is rewarded while seeking the common good is not. Maynard Smith, a mathematical biologist, turned to game theory as suggested by George Price, though Richard Lewontin's attempts to use the theory had failed.^[6]

Adapting game theory to evolutionary games

Maynard Smith realised that an evolutionary version of game theory does not require players to act rationally – only that they have a strategy. The results of a game shows how good that strategy was, just as evolution tests alternative strategies for the ability to survive and reproduce. In biology, strategies are genetically inherited traits that control an individual's action, analogous with computer programs. The success of a strategy is determined by how good the strategy is in the presence of competing strategies (including itself), and of the frequency with which those strategies are used.^[7] Maynard Smith described his work in his book Evolution and the Theory of Games.^[8]

Participants aim to produce as many replicas of themselves as they can, and the payoff is in units of fitness (relative worth in being able to reproduce). It is always a multi-player game with many competitors. Rules include replicator dynamics, in other words how the fitter players will spawn more replicas of themselves into 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 reproduction for the sake of simplicity. Games are run repetitively with no terminating conditions. Results include the dynamics of changes in the population, the success of strategies, and any equilibrium states reached. Unlike in classical game theory, players do not choose their strategy and cannot change it: they are born with a strategy and their offspring inherit that same strategy.^[9]

Evolutionary games

Models

Evolutionary game theory analyses Darwinian mechanisms with a system model with three main components – Population, Game, and Replicator Dynamics. The system process has four phases:

1) The model (as evolution itself) deals with a Population (Pn). The population will exhibit Variation among Competing individuals. In the model this competition is represented by the Game.

2) The Game tests the strategies of the individuals under the “rules of the game”. These rules produce different payoffs – in units of Fitness (the production rate of offspring). The contesting individuals meet in pairwise contests with others, normally in a highly mixed distribution of the population. The mix of strategies in the population affects the payoff results by altering the odds that any individual may meet up in contests with various strategies. The individuals leave the game pairwise contest with a resulting fitness determined by the contest outcome, represented in a Payoff Matrix.

3) Based on this resulting fitness each member of the population then undergoes replication or culling determined by the exact mathematics of the Replicator Dynamics Process. This overall process then produces a New Generation P(n+1). Each surviving individual now has a new fitness level determined by the game result.

4) The new generation then takes the place of the previous one and the cycle repeats. The population mix may converge to an Evolutionarily Stable State that cannot be invaded by any mutant strategy.

EGT encompasses Darwinian evolution, including competition (the game), natural selection (replicator dynamics), and heredity. EGT has contributed to the understanding of group selection, sexual selection, altruism, parental care, co-evolution, and ecological dynamics. Many counter-intuitive situations in these areas have been put on a firm mathematical footing by the use of these models.^[10]

The common way to study the evolutionary dynamics in games is through replicator equations. These show the growth rate of the proportion of organisms using a certain strategy and that rate is equal to the difference between the average payoff of that strategy and the average payoff of the population as a whole.^[11] Continuous replicator equations assume infinite populations, continuous time, complete mixing and that strategies breed true. The attractors (stable fixed points) of the equations are equivalent with evolutionarily stable states. A strategy which can survive all "mutant" strategies is considered evolutionarily stable. In the context of animal behavior, this usually means such strategies are programmed and heavily influenced by genetics, thus making any player or organism's strategy determined by these biological factors.^[12][13]

Evolutionary games are mathematical objects with different rules, payoffs, and mathematical behaviours. Each "game" represents different problems that organisms have to deal with, and the strategies they might adopt to survive and reproduce. Evolutionary games are often given colourful names and cover stories which describe the general situation of a particular game. Representative games include hawk-dove,^[1] war of attrition,^[14] stag hunt, producer-scrounger, tragedy of the commons, and prisoner's dilemma. Strategies for these games include Hawk, Dove, Bourgeois, Prober, Defector, Assessor, and Retaliator. The various strategies compete under the particular game's rules, and the mathematics are used to determine the results and behaviours.

Hawk Dove

Solution of the Hawk Dove game for V=2, C=10 and fitness starting base B=4. The fitness of a Hawk for different population mixes is plotted as a black line, that of Dove in red. An ESS (a stationary point) will exist when Hawk and Dove fitness are equal: Hawks are 20% of population and Doves are 80% of the population.

The first game that Maynard Smith analysed is the classic Hawk Dove^[a] game. It was conceived to analyse Lorenz and Tinbergen's problem, a contest over a shareable resource. The contestants can be either Hawk or Dove. These are two subtypes or morphs of one species with different strategies. The Hawk first displays aggression, then escalates into a fight until it either wins or is injured (loses). The Dove first displays aggression, but if faced with major escalation runs for safety. If not faced with such escalation, the Dove attempts to share the resource.^[1]
 

Payoff Matrix for Hawk Dove Game

	meets Hawk	meets Dove
if Hawk	V/2 − C/2	V
if Dove	0	V/2

Given that the resource is given the value V, the damage from losing a fight is given cost C:^[1]

• If a Hawk meets a Dove he gets the full resource V to himself
• If a Hawk meets a Hawk – half the time he wins, half the time he loses...so his average outcome is then V/2 minus C/2
• If a Dove meets a Hawk he will back off and get nothing – 0
• If a Dove meets a Dove both share the resource and get V/2

The actual payoff however depends on the probability of meeting a Hawk or Dove, which in turn is a representation of the percentage of Hawks and Doves in the population when a particular contest takes place. That in turn is determined by the results of all of the previous contests. If the cost of losing C is greater than the value of winning V (the normal situation in the natural world) the mathematics ends in an ESS, a mix of the two strategies where the population of Hawks is V/C. The population regresses to this equilibrium point if any new Hawks or Doves make a temporary perturbation in the population. The solution of the Hawk Dove Game explains why most animal contests involve only ritual fighting behaviours in contests rather than outright battles. The result does not at all depend on good of the species behaviours as suggested by Lorenz, but solely on the implication of actions of so-called selfish genes.^[1]

War of attrition

In the Hawk Dove game the resource is shareable, which gives payoffs to both Doves meeting in a pairwise contest. Where the resource is not shareable, but an alternative resource might be available by backing off and trying elsewhere, pure Hawk or Dove strategies are less effective. If an unshareable resource is combined with a high cost of losing a contest (injury or possible death) both Hawk and Dove payoffs are further diminished. A safer strategy of lower cost display, bluffing and waiting to win, is then viable – a Bluffer strategy. The game then becomes one of accumulating costs, either the costs of displaying or the costs of prolonged unresolved engagement. It is effectively an auction; the winner is the contestant who will swallow the greater cost while the loser gets the same cost as the winner but no resource.^[14] The resulting evolutionary game theory mathematics leads to an optimal strategy of timed bluffing.^[15]

War of attrition for different values of resource. Note the time it takes for an accumulation of 50% of the contestants to quit vs. the Value(V) of resource contested for.

This is because in the war of attrition any strategy that is unwavering and predictable is unstable, because it will ultimately be displaced by a mutant strategy which relies on the fact that it can best the existing predictable strategy by investing an extra small delta of waiting resource to ensure that it wins. Therefore, only a random unpredictable strategy can maintain itself in a population of Bluffers. The contestants in effect choose an acceptable cost to be incurred related to the value of the resource being sought, effectively making a random bid as part of a mixed strategy (a strategy where a contestant has several, or even many, possible actions in his strategy). This implements a distribution of bids for a resource of specific value V, where the bid for any specific contest is chosen at random from that distribution. The distribution (an ESS) can be computed using the Bishop-Cannings theorem, which holds true for any mixed strategy ESS.^[16] The distribution function in these contests was determined by Parker and Thompson to be:

${\displaystyle p(x)={\frac {e^{-x/V}}{V}}.}$

The result is that the cumulative population of quitters for any particular cost m in this "mixed strategy" solution is:

${\displaystyle p(m)=1-e^{-m/V},}$

as shown in the adjacent graph. The intuitive sense that greater values of resource sought leads to greater waiting times is borne out. This is observed in nature, as in male dung flies contesting for mating sites, where the timing of disengagement in contests is as predicted by evolutionary theory mathematics.^[17]

Asymmetries that allow new strategies

Dung Fly (Scatophaga stercoraria) – a War of Attrition player

The mantis shrimp guarding its home with the Bourgeois Strategy

 

Animal Strategy Examples: by examining the behaviours, then determining both the Costs and the Value of resources attained in a contest the strategy of an organism can be verified

In the War of Attrition there must be nothing that signals the size of a bid to an opponent, otherwise the opponent can use the cue in an effective counter-strategy. There is however a mutant strategy which can better a Bluffer in the War of Attrition Game if a suitable asymmetry exists, the Bourgeois strategy. Bourgeois uses an asymmetry of some sort to break the deadlock. In nature one such asymmetry is possession of a resource. The strategy is to play a Hawk if in possession of the resource, but to display then retreat if not in possession. This requires greater cognitive capability than Hawk, but Bourgeois is common in many animal contests, such as in contests among mantis shrimps and among speckled wood butterflies.

Social behaviour

Alternatives for game theoretic social interaction

Games like Hawk Dove and War of Attrition represent pure competition between individuals and have no attendant social elements. Where social influences apply, competitors have four possible alternatives for strategic interaction. This is shown on the adjacent figure, where a plus sign represents a benefit and a minus sign represents a cost.

• In a Cooperative or Mutualistic relationship both "donor" and "recipient" are almost indistinguishable as both gain a benefit in the game by co-operating, i.e. the pair are in a game-wise situation where both can gain by executing a certain strategy, or alternatively both must act in concert because of some encompassing constraints that effectively puts them "in the same boat".
• In an Altruistic relationship the donor, at a cost to himself provides a benefit to the recipient. In the general case the recipient will have a kin relationship to the donor and the donation is one-way. Behaviours where benefits are donated alternatively (in both directions) at a cost, are often called altruistic, but on analysis such "altruism" can be seen to arise from optimised "selfish" strategies
• Spite is essentially a "reversed" form of altruism where an ally is aided by damaging the ally's competitor(s). The general case is that the ally is kin related and the benefit is an easier competitive environment for the ally. Note: George Price, one of the early mathematical modellers of both altruism and spite, found this equivalence particularly disturbing at an emotional level.^[18]
• Selfishness is the base criteria of all strategic choice from a game theory perspective – strategies not aimed at self-survival and self-replication are not long for any game. Critically however, this situation is impacted by the fact that competition is taking place on multiple levels – i.e. at a genetic, an individual and a group level.

Contests of selfish genes

Female Belding's ground squirrels risk their lives giving loud alarm calls, protecting closely related female colony members; males are less closely related and do not call.^[19]

At first glance it may appear that the contestants of evolutionary games are the individuals present in each generation who directly participate in the game. But individuals live only through one game cycle, and instead it is the strategies that really contest with one another over the duration of these many-generation games. So it is ultimately genes that play out a full contest – selfish genes of strategy. The contesting genes are present in an individual and to a degree in all of the individual's kin. This can sometimes profoundly affect which strategies survive, especially with issues of cooperation and defection. William Hamilton,^[20] known for his theory of kin selection, explored many of these cases using game theoretic models. Kin related treatment of game contests^[21] helps to explain many aspects of the behaviour of social insects, the altruistic behaviour in parent/offspring interactions, mutual protection behaviours, and co-operative care of offspring. For such games Hamilton defined an extended form of fitness – inclusive fitness, which includes an individual's offspring as well as any offspring equivalents found in kin.

The Mathematics of Kin Selection

The concept of Kin Selection is that: inclusive fitness=own contribution to fitness +                             contribution of all relatives. Fitness is measured relative to the average population; for example, fitness=1 means growth at the average rate for the population, fitness < 1 means having a decreasing share in the population (dying out), fitness > 1 means an increasing share in the population (taking over). The inclusive fitness of an individual wi is the sum of its specific fitness of itself ai plus the specific fitness of each and every relative weighted by the degree of relatedness which equates to the summation of all rj*bj....... where rj is relatedness of a specific relative and bj is that specific relative's fitness – producing: ${\displaystyle w_{i}=a_{i}+\sum _{j}r_{j}b_{j}.}$ Now if individual ai sacrifices his "own average equivalent fitness of 1" by accepting a fitness cost C, and then to "get that loss back", wi must still be 1 (or greater than 1)...and if we use R*B to represent the summation we get: 1< (1-C)+RB ....or rearranging..... R>C/B.[22]

Hamilton went beyond kin relatedness to work with Robert Axelrod, analysing games of co-operation under conditions not involving kin where reciprocal altruism comes into play.^[23]

Eusociality and kin selection

Meat ant workers (always female) are related To mother or father=0.5 To sister+=0.75 To own daughter or son=0.5 To brother=0.25....... Therefore, it is more advantageous to help produce a sister than to have a child oneself.

Eusocial insect workers forfeit reproductive rights to their queen. It has been suggested that Kin Selection, based on the genetic makeup of these workers, may predispose them to altruistic behaviour.^[24] Most eusocial insect societies have haplodiploid sexual determination, which means that workers are unusually closely related.^[25]

This explanation of insect eusociality has however been challenged by a few highly noted evolutionary game theorists (Nowak and Wilson)^[26] who have published a controversial alternative game theoretic explanation based on a sequential development and group selection effects proposed for these insect species.^[27]

Prisoner's dilemma

A difficulty of the theory of evolution, recognised by Darwin himself, was the problem of altruism. If the basis for selection is at individual level, altruism makes no sense at all. But universal selection at the group level (for the good of the species, not the individual) fails to pass the test of the mathematics of game theory and is certainly not the general case in nature.^[28] Yet in many social animals, altruistic behaviour exists. The solution to this paradox can be found in the application of evolutionary game theory to the prisoner's dilemma game – a game which tests the payoffs of cooperating or in defecting from cooperation. It is certainly the most studied game in all of game theory.^[29]
The analysis of prisoner's dilemma is as a repetitive game. This affords competitors the possibility of retaliating for defection in previous rounds of the game. Many strategies have been tested; the best competitive strategies are general cooperation with a reserved retaliatory response if necessary.^[30] The most famous and one of the most successful of these is tit-for-tat with a simple algorithm.

procedure tit-for-tat
EventBit:=Trust;

do while Contest=ON;
    if Eventbit=Trust then
        Cooperate 
    else
        Defect;
    
    if Opponent_Move=Cooperate then 
        EventBit:=Trust 
    else 
        Eventbit:=NOT(Trust);
end;

The pay-off for any single round of the game is defined by the pay-off matrix for a single round game (shown in bar chart 1 below). In multi-round games the different choices – Co-operate or Defect – can be made in any particular round, resulting in a certain round payoff. It is, however, the possible accumulated pay-offs over the multiple rounds that count in shaping the overall pay-offs for differing multi-round strategies such as Tit-for-Tat.

Payoffs in two varieties of prisoner's dilemma game.
Prisoner's dilemma: Co-operate or Defect?
Payoff _{(Temptation in Defecting vs. Co-operation)} > Payoff _{(Mutual Co-operation)} > Payoff_{(Joint Defection)} > Payoff_{(Sucker co-operates but opponent defects)}

Example 1: The straightforward single round prisoner's dilemma game. The classic prisoner's dilemma game payoffs gives a player a maximum payoff if he defect and his partner co-operates (this choice is known as temptation). If however the player co-operates and his partner defects, he gets the worst possible result (the suckers payoff). In these payoff conditions the best choice (a Nash equilibrium) is to defect.

Example 2: Prisoner's dilemma played repeatedly. The strategy employed is Tit-for-Tat which alters behaviors based on the action taken by a partner in the previous round – i.e. reward co-operation and punish defection. The effect of this strategy in accumulated payoff over many rounds is to produce a higher payoff for both players co-operation and a lower payoff for defection. This removes the Temptation to defect. The suckers payoff also becomes less, although "invasion" by a pure defection strategy is not entirely eliminated.

Routes to altruism

Altruism takes place when one individual, at a cost C to itself, exercises a strategy that provides a benefit B to another individual. The cost may consist of a loss of capability or resource which helps in the battle for survival and reproduction, or an added risk to its own survival. Altruism strategies can arise through:

Type	Applies to:	Situation	Mathematical effect
Kin Selection – (inclusive fitness of related contestants)	Kin – genetically related individuals	Evolutionary Game participants are genes of strategy. The best payoff for an individual is not necessarily the best payoff for the gene. In any generation the player gene is NOT only in one individual, it is in a Kin-Group. The highest fitness payoff for the Kin Group is selected by natural selection. Therefore, strategies that include self-sacrifice on the part of individuals are often game winners – the evolutionarily stable strategy. Animals must live in kin-group during part of the game for the opportunity for this altruistic sacrifice ever to take place.	Games must take into account Inclusive Fitness. Fitness function is the combined fitness of a group of related contestants – each weighted by the degree of relatedness – relative to the total genetic population. The mathematical analysis of this gene centric view of the game leads to Hamilton's rule, that the relatedness of the altruistic donor must exceed the cost-benefit ratio of the altruistic act itself:[31] R>c/b R is relatedness, c the cost, b the benefit
Direct reciprocity	Contestants that trade favours in paired relationships	A game theoretic embodiment of "I'll scratch your back if you scratch mine". A pair of individuals exchange favours in a multi-round game. The individuals are recognisable to one another as partnered. The term "direct" applies because the return favour is specifically given back to the pair partner only.	The characteristics of the multi-round game produce a danger of defection and the potentially lesser payoffs of cooperation in each round, but any such defection can lead to punishment in a following round – establishing the game as repeated prisoner's dilemma. Therefore, the family of tit-for-tat strategies come to the fore.[32]
Indirect Reciprocity	Related or non related contestants trade favours but without partnering. A return favour is "implied" but with no specific identified source who is to give it.	This behaviour is akin to "I'll scratch your back, you scratch someone else's back, another someone else will scratch mine (probably)". The return favour is not derived from any particular established partner. The potential for indirect reciprocity exists for a specific organism if it lives in a cluster of individuals who can interact over an extended period of time. It has been argued that human behaviours in establishing moral system as well as the expending of significant energies in human society for tracking individual reputation is a direct effect of societies reliance on strategies of indirect reciprocation.[33]	The game is highly susceptible to defection, as direct retaliation is impossible. Therefore, indirect reciprocity will not work without keeping a social score, a measure of past co-operative behaviour. The mathematics leads to a modified version of Hamilton's Rule where: q>c/b where q (the probability of knowing the social score) must be greater than the cost benefit ratio[34][35] Organisms that use social score are termed Discriminators, and require a higher level of cognition than strategies of simple direct reciprocity. As evolutionary biologist David Haig put it – "For direct reciprocity you need a face; for indirect reciprocity you need a name".

The evolutionarily stable strategy

The Payoff Matrix for the Hawk Dove Game with the addition of the Assessor Strategy. This "studies its opponent", behaving as a Hawk when matched with an opponent it judges "weaker", like a Dove when the opponent seems bigger and stronger. Assessor is an ESS, since it can invade both Hawk and Dove populations, and can withstand invasion by either Hawk or Dove mutants.

The evolutionarily stable strategy (ESS) is akin to Nash equilibrium in classical game theory, but with mathematically extended criteria. Nash Equilibrium is a game equilibrium where it is not rational for any player to deviate from their present strategy. An ESS is a state of game dynamics where, in a very large population of competitors, another mutant strategy cannot successfully enter the population to disturb the existing dynamic (which itself depends on the population mix). Therefore, a successful strategy (with an ESS) must be both effective against competitors when it is rare – to enter the previous competing population, and successful when later in high proportion in the population – to defend itself. This in turn means that the strategy must be successful when it contends with others exactly like itself.^[36][37][38]

An ESS is not:

• An optimal strategy: that would maximize Fitness, and many ESS states are far below the maximum fitness achievable in a fitness landscape. (see Hawk Dove graph above as an example of this)
• A singular solution: often several ESS conditions can exist in a competitive situation. A particular contest might stabilize into any one of these possibilities, but later a major perturbation in conditions can move the solution into one of the alternative ESS states.
• Always present: it is possible for there to be no ESS. An evolutionary game with no ESS is Rock-Scissors-Paper, as found in species such as the side-blotched lizard (Uta stansburiana).
• An unbeatable strategy: the ESS is only an uninvadeable strategy.

Female funnel web spiders (Agelenopsis aperta) contest with one another for the possession of their desert spider webs using the Assessor strategy.^[39]

The ESS state can be solved for by exploring either the dynamics of population change to determine an ESS, or by solving equations for the stable stationary point conditions which define an ESS.^[40] For example, in the Hawk Dove Game we can look for whether there is a static population mix condition where the fitness of Doves will be exactly the same as fitness of Hawks (therefore both having equivalent growth rates – a static point).

Let the chance of meeting a Hawk=p so therefore the chance of meeting a dove is (1-p)

Let WHawk equal the Payoff for Hawk.....

WHawk=Payoff in the chance of meeting a Dove + Payoff in the chance of meeting a Hawk

Taking the PAYOFF MATRIX results and plugging them into the above equation:

WHawk= V·(1-p)+(V/2-C/2)·p

Similarly for a Dove:

WDove= V/2·(1-p)+0·(p)

so....

WDove= V/2·(1-p)

Equating the two fitnesses, Hawk and Dove

V·(1-p)+(V/2-C/2)·p= V/2·(1-p)

... and solving for p

p= V/C

so for this "static point" where the Population Percent is an ESS solves to be ESS_{(percent Hawk)}=V/C

Similarly, using inequalities, it can be shown that an additional Hawk or Dove mutant entering this ESS state eventually results in less fitness for their kind – both a true Nash and an ESS equilibrium. This example shows that when the risks of contest injury or death (the Cost C) is significantly greater than the potential reward (the benefit value V), the stable population will be mixed between aggressors and doves, and the proportion of doves will exceed that of the aggressors. This explains behaviours observed in nature.

Unstable games, cyclic patterns

Rock-paper-scissors

Rock Paper Scissors

Mutant Invasion for Rock Paper Scissors payoff matrix – an endless cycle

An evolutionary game that turns out to be a children's game is rock-paper-scissors. The game is simple – rock beats scissors (blunts it), scissors beats paper (cuts it), and paper beats rock (wraps it up). Anyone who has ever played this simple game knows that it is not sensible to have any favoured play – the opponent will soon notice this and switch to the winning counter-play. The best strategy (a Nash equilibrium) is to play a mixed random game with any of the three plays taken a third of the time. This, in EGT terms, is a mixed strategy. But many lifeforms are incapable of mixed behavior – they only exhibit one strategy (known as a pure strategy). If the game is played only with the pure Rock, Paper and Scissors strategies the evolutionary game is dynamically unstable: Rock mutants can enter an all scissor population, but then – Paper mutants can take over an all Rock population, but then – Scissor mutants can take over an all Paper population – and on and on.... This is easily seen on the game payoff matrix, where if the paths of mutant invasion are noted, it can be seen that the mutant "invasion paths" form into a loop. This in triggers a cyclic invasion pattern.

A computer simulation of the Rock Scissors Paper game. The associated RPS Game Payoff Matrix is shown. Starting with an arbitrary population the percentage of the three morphs builds up into a continuously cycling pattern.

Rock-paper-scissors incorporated into an evolutionary game has been used for modelling natural processes in the study of ecology.^[41] Using experimental economics methods, scientists have used RPS game to test human social evolutionary dynamical behaviors in laboratory. The social cyclic behaviors, predicted by evolutionary game theory, have been observed in various laboratory experiments.^[42][43]

The side-blotched lizard

The side-blotched lizard (Uta stansburiana) is polymorphic with three morphs^[44] that each pursues a different mating strategy.

The side-blotched lizard effectively uses a rock-paper-scissors mating strategy.

1) The orange throat is very aggressive and operates over a large territory – attempting to mate with numerous females within this larger area

2) The unaggressive yellow throat mimics the markings and behavior of female lizards, and "sneakily" slips into the orange throat's territory to mate with the females there (thereby taking over the population), and

3) The blue throat mates with and carefully guards one female – making it impossible for the sneakers to succeed and therefore overtakes their place in a population…

However the blue throats cannot overcome the more aggressive orange throats. The overall situation corresponds to the Rock, Scissors, Paper game, creating a six-year population cycle. When he read that these lizards were essentially engaged in a game with rock-paper-scissors structure, John Maynard Smith is said to have exclaimed "They have read my book!"^[45]

Signalling, sexual selection and the handicap principle

The peacock's tail may be an instance of the handicap principle in action.

Aside from the difficulty of explaining how altruism exists in many evolved organisms, Darwin was also bothered by a second conundrum – why do a significant number of species have phenotypical attributes that are patently disadvantageous to them with respect to their survival – and should by the process of natural section be selected against – e.g. the massive inconvenient feather structure found in a peacock's tail? Regarding this issue Darwin wrote to a colleague "The sight of a feather in a peacock's tail, whenever I gaze at it, makes me sick."^[46] It is the mathematics of evolutionary game theory, which has not only explained the existence of altruism but also explains the totally counterintuitive existence of the peacock's tail and other such biological encumbrances.

On analysis, problems of biological life are not at all unlike the problems that define economics – eating (akin to resource acquisition and management), survival (competitive strategy) and reproduction (investment, risk and return). Game theory was originally conceived as a mathematical analysis of economic processes and indeed this is why it has proven so useful in explaining so many biological behaviours. One important further refinement of the EGT model that has economic overtones rests on the analysis of COSTS. A simple model of cost assumes that all competitors suffer the same penalty imposed by the Game costs, but this is not the case. More successful players will be endowed with or will have accumulated a higher "wealth reserve" or "affordability" than less successful players. This wealth effect in evolutionary game theory is represented mathematically by "resource holding potential (RHP)" and shows that the effective cost to a competitor with higher RHP are not as great as for a competitor with a lower RHP. As a higher RHP individual is more desirable mate in producing potentially successful offspring, it is only logical that with sexual selection RHP should have evolved to be signalled in some way by the competing rivals, and for this to work this signalling must be done honestly. Amotz Zahavi has developed this thinking in what is known as the handicap principle,^[47] where superior competitors signal their superiority by a costly display. As higher RHP individuals can properly afford such a costly display this signalling is inherently honest, and can be taken as such by the signal receiver. Nowhere in nature is this better illustrated than in the magnificent and costly plumage of the peacock. The mathematical proof of the handicap principle was developed by Alan Grafen using evolutionary game-theoretic modelling.^[48]

Co-evolution

Two types of dynamics have been discussed so far in this article:

• Evolutionary games which lead to a stable situation or point of stasis for contending strategies which result in an evolutionarily stable strategy
• Evolutionary games which exhibit a cyclic behaviour (as with RPS game) where the proportions of contending strategies continuously cycle over time within the overall population

Competitive Co-evolution - The rough-skinned newt (Tarricha granulosa) is highly toxic, due to an evolutionary arms race with a predator, the common garter snake (Thamnophis sirtalis), which in turn is highly tolerant of the poison. The two are locked in a Red Queen arms race.^[49]

Mutualistic Coevolution - Darwin's orchid (Angraecum sesquipedale) and the moth Morgan's sphinx (Xanthopan morgani) have a mutual relationship where the moth gains pollen and the flower is pollinated.

A third, co-evolutionary, dynamic combines intra-specific and inter-specific competition. Examples include predator-prey competition and host-parasite co-evolution, as well as mutualism. Evolutionary game models have been created for pairwise and multi-species coevolutionary systems.^[50] The general dynamic differs between competitive systems and mutualistic systems.

In competitive (non-mutualistic) inter-species coevolutionary system the species are involved in an arms race – where adaptations that are better at competing against the other species tend to be preserved. Both game payoffs and replicator dynamics reflect this. This leads to a Red Queen dynamic where the protagonists must "run as fast as they can to just stay in one place".^[51]

A number of EGT models have been produced to encompass coevolutionary situations. A key factor applicable in these coevolutionary systems is the continuous adaptation of strategy in such arms races. Coevolutionary modelling therefore often includes genetic algorithms to reflect mutational effects, while computers simulate the dynamics of the overall coevolutionary game. The resulting dynamics are studied as various parameters are modified. Because several variables are simultaneously at play, solutions become the province of multi-variable optimisation. The mathematical criteria of determining stable points are Pareto efficiency and Pareto dominance, a measure of solution optimality peaks in multivariable systems.^[52]

Carl Bergstrom and Michael Lachmann apply evolutionary game theory to the division of benefits in mutualistic interactions between organisms. Darwinian assumptions about fitness are modeled using replicator dynamics to show that the organism evolving at a slower rate in a mutualistic relationship gains a disproportionately high share of the benefits or payoffs.^[53]

Extending the model

A mathematical model analysing the behaviour of a system needs initially to be as simple as possible to aid in developing a base understanding the fundamentals, or “first order effects”, pertaining to what is being studied. With this understanding in place it is then appropriate to see if other, more subtle, parameters (second order effects) further impact the primary behaviours or shape additional behaviours in the system. Following Maynard Smith’s seminal work in EGT, the subject has had a number of very significant extensions which have shed more light on understanding evolutionary dynamics, particularly in the area of altruistic behaviors. Some of these key extensions to EGC are:

A Spatial Game
In a spatial evolutionary game contestants meet in contests at fixed grid positions and only interact with immediate neighbors. Shown here are the dynamics of a Hawk Dove contest, showing Hawk and Dove contestants as well as the changes of strategy taking place in the various cells

 

Spatial Games	Geographic factors in evolution include gene flow and horizontal gene transfer. Spatial game models represent geometry by putting contestants in a lattice of cells: contests take place only with immediate neighbours. Winning strategies take over these immediate neighbourhoods and then interact with adjacent neighbourhoods. This model is useful in showing how pockets of co-operators can invade and introduce altruism in the Prisoners Dilemma game,[54] where Tit for Tat (TFT) is a Nash Equilibrium but NOT also an ESS. Spatial structure is sometimes abstracted into a general network of interactions.[55][56] This is the foundation of evolutionary graph theory.
Effects of having information	In EGT as in conventional Game Theory the effect of Signalling (the acquisition of information) is of critical importance, as in Indirect Reciprocity in Prisoners Dilemma (where contests between the SAME paired individuals are NOT repetitive). This models the reality of most normal social interactions which are non-kin related. Unless a probability measure of reputation is available in Prisoners Dilemma only direct reciprocity can be achieved.[31] With this information indirect reciprocity is also supported. Alternatively, agents might have access to an arbitrary signal initially uncorrelated to strategy but becomes correlated due to evolutionary dynamics. This is the green-beard effect or evolution of ethnocentrism in humans.[57] Depending on the game, it can allow the evolution of either cooperation or irrational hostility.[58] From molecular to multicellular level, a signaling game model with information asymmetry between sender and receiver might be appropriate, such as in mate attraction[48] or evolution of translation machinery from RNA strings.[59]
Finite populations	Many evolutionary games have been modelled in finite populations to see the effect this may have, for example in the success of mixed strategies.