Cheating (biology)

From Wikipedia, the free encyclopedia

Cheating is a term used in behavioral ecology and ethology to describe behavior whereby organisms receive a benefit at the cost of other organisms. Cheating is common in many mutualistic and altruistic relationships. A cheater is an individual who does not cooperate (or cooperates less than their fair share) but can potentially gain the benefit from others cooperating. Cheaters are also those who selfishly use common resources to maximize their individual fitness at the expense of a group. Natural selection favors cheating, but there are mechanisms to regulate it.

Theoretical models

Organisms communicate and cooperate to perform a wide range of behaviors. Mutualism, or mutually beneficial interactions between species, is common in ecological systems. These interactions can be thought of "biological markets" in which species offer partners goods that are relatively inexpensive for them to produce and receive goods that are more expensive or even impossible for them to produce. However, these systems provide opportunities for exploitation by individuals that can obtain resources while providing nothing in return. Exploiters can take on several forms: individuals outside a mutualistic relationship who obtain a commodity in a way that confers no benefit to either mutualist, individuals who receive benefits from a partner but have lost the ability to give any in return, or individuals who have the option of behaving mutualistically towards their partners but chose not to do so.

Cheaters, who do not cooperate but benefit from others who do cooperate, gain a competitive edge. In an evolutionary context, this competitive edge refers to a greater ability to survive or to reproduce. If individuals who cheat are able to gain survivorship and reproductive benefits while incurring no costs, natural selection should favor cheaters. What then prevents cheaters from undermining mutualistic systems? One main factor is that the advantages of cheating are often frequency-dependent. Frequency-dependent selection occurs when the fitness of a phenotype depends on its frequency relative to other phenotypes in a population. Cheater phenotypes often display negative frequency-dependent selection, where fitness increases as a phenotype becomes less common and vice versa. In other words, cheaters do best (in terms of evolutionary benefits such as increased survival and reproduction) when there are relatively few of them, but as cheaters become more abundant, they do worse.

For example, in Escherichia coli colonies, there are antibiotic-sensitive "cheaters" that persist at low numbers on antibiotic-laced mediums when in a cooperative colony. These cheaters enjoy the benefit of others producing antibiotic-resistant agents while producing none themselves. However, as numbers increase, if they persist in not producing the antibiotic agent themselves, they are more likely to be negatively impacted by the antibiotic substrate because there is less antibiotic agent to protect everyone. Thus, cheaters can persist in a population because their exploitative behavior gives them an advantage when they exist at low frequencies but these benefits are diminished when they are greater in number.

Others have proposed that cheating (exploitive behavior) can stabilize cooperation in mutualistic systems. In many mutualistic systems, there will be feedback benefits to those that cooperate. For instance, the fitness of both partners may be improved. If there is a high reward or many benefits for the individual that initiated the cooperative behavior, mutualism should be selected for. When researchers investigated the co-evolution of cooperation and choice in a choosy host and its symbiont (an organism that lives in a relationship that benefits all parties involved), their model indicated that although choice and cooperation may be initially selected for, this would often be unstable. In other words, one cooperative partner will choose another cooperative partner if given a choice. However, if this choice is made over and over, variation is removed and this selection can no longer be maintained. This situation is similar to the lek paradox in female choice. For example, in lek paradox, if females consistently choose for a particular male trait, genetic variance for that trait should eventually be eliminated, removing the benefits of choice. However, that choice somehow still persists.

What maintains genetic variability in the face of selection for mutualism (cooperative behavior)? One theory is that cheating maintains this genetic variation. One study shows that a small influx of immigrants with a tendency to cooperate less can generate enough genetic variability to stabilize selection for mutualism. This suggests that the presence of exploitive individuals, otherwise known as cheaters, contribute enough genetic variation to maintain mutualism itself. Both this theory and the negative frequency-dependent theory suggest that that cheating exists as part of a stable mixed evolutionary strategy with mutualism. In other words, cheating is a stable strategy used by individuals in a population where many other individuals cooperate. Another study supports that cheating can exist as a mixed strategy with mutualism using a mathematical game model. Thus, cheating can arise and be maintained in mutualistic populations.

Examples

Stalked slime mould fruiting bodies

Studies of cheating and dishonest communication in populations presupposes an organismal system that cooperates. Without a collective population that has signaling and interactions among individuals, behaviors such as cheating do not manifest. In other words, in order to study cheating behavior, a model system that engages in cooperation is needed. Models that provide insight on cheating include the social amoeba Dictyostelium discoideum; eusocial insects, such as ants, bees, and wasps; and inter-specific interactions found in cleaning mutualisms. Common examples of cleaning mutualisms include cleaner fish such as wrasses and gobies, and some cleaner shrimp.

In Dictyostelium discoideum

Dictyostelium discoideum is a widely used model for cooperation and the development of multicellularity. This species of amoeba are most commonly found in a haploid, single-celled state that feed independently and undergo asexual reproduction. However, when the scarcity of food sources cause individual cells to starve, roughly 10⁴ to 10⁵ cells aggregate to form a mobile, multicellular structure dubbed a "slug". In the wild, aggregates generally contain multiple genotypes, resulting in chimeric mixtures. Unlike clonal (genetically identical) aggregates typically found in multicellular organisms, the potential for competition exists in chimeric aggregates. For example, because individuals in the aggregate contain different genomes, differences in fitness can result in conflict of interest among cells in the aggregate, where different genotypes could potentially compete against each other for resources and reproduction. In Dictyostelium discoideum, roughly 20% of the cells in the aggregate become dead to make the stalk of a fruiting body. The remaining 80% of cells become spores in the sorus of the fruiting body, which can germinate again once conditions are more favorable. In this case, 20% of the cells must give up reproduction so that fruiting body forms successfully. This makes chimeric aggregates of Dictyostelium discoideum susceptible to cheating individuals that take advantage of the reproductive behavior without paying the fair price. In other words, if certain individuals tend to become a part of the sorus more frequently, they can gain increased benefit from the fruiting body system without sacrificing their own opportunities to reproduce. Cheating behavior in D. discoideum is well established, and many studies have attempted to elucidate the evolutionary and genetic mechanisms underlying the behavior. Having a 34Mb genome that is completely sequenced and well annotated makes D. discoideum a useful model in studying the genetic bases and molecular mechanisms of cheating, and in a broader sense, social evolution.

In eusocial insects

Eusocial insects also serve as valuable tools in studying cheating. Eusocial insects behave cooperatively, where members of the community forgo reproduction to assist a few individuals to reproduce. Such model systems have potential for conflict of interest to arise among individuals, and thus also have potential for cheating to occur. Eusocial insects in the order Hymenoptera, which includes bees and wasps, exhibit good examples of conflicts of interest present in insect societies. In these systems, queen bees and wasps can mate and lay fertilized eggs that hatch into females. On the other hand, workers of most species in Hymenoptera can produce eggs, but cannot produce fertilized eggs due to loss of mating ability. Workers that lay eggs represent a cost for the colony because workers that lay eggs often do significantly less work, and thus negatively impact the health of the colony (for example: decreased amount of collected food, or less attention given to tending the queen's eggs). In this case, a conflict of interest arises between the workers and the colony. The workers should lay eggs in order to pass on their genes; however, as a colony, having only the queen reproduce leads to better productivity. If workers sought to pass their own genes by laying eggs, foraging activities would diminish, leading to decreased resources for the entire colony. This, in turn, can cause a tragedy of the commons, where selfish behavior lead to the depletion of resources, with long-term negative consequences for the group. However, in natural bee and wasp societies, only 0.01–0.1% and 1%, respectively, of the workers lay eggs, suggesting that strategies exist to combat cheating to prevent tragedy of the commons. These insect systems have given scientists opportunities to study strategies that keep cheating in check. Such strategies are commonly referred to as "policing" strategies, generally where additional costs are imposed on cheaters to discourage or eliminate cheating behaviors. For example, honeybees and wasps may eat eggs produced by workers. In some ant species and yellowjackets, policing may occur via aggression towards or killing egg-laying individuals to minimize cheating.

Fish cleaned by smaller cleaner wrasses on Hawaiian reefs

In cleaning symbiosis

Cleaning symbiosis that develop between small and larger marine organisms often represent models useful for studying the evolution of stable social interactions and cheating. In the cleaning fish Labroides dimidiatus (Bluestreak cleaner wrasse), as in many cleaner species, client fish seeks to have ectoparasites removed by the cleaners. In these situations, instead of picking off the parasites on the surface of the client fish, the cleaner can cheat by feeding on the client's tissue (mucus layer, scales, etc.), thereby gaining additional benefit from the symbiotic system. It has been well documented that cleaners will feed on mucus when their clients are unable to control the cleaner's behavior; however, in natural settings, client fish often jolt, chase after cheating cleaners, or terminate interactions of swimming way, effectively controlling the cheating behavior. Studies on cleaning mutualisms generally suggest that cheating behavior is often adjusted depending on the species of the client. In cleaning shrimp, cheating is predicted to occur less often because shrimps bear a higher cost if the clients use aggression to control the cleaner's behavior. Studies have found that cleaner species can strategically adjust cheating behavior according to the potential associated risk. For example, predatory clients, which present a significantly high cost for cheating, experience less cheating behavior. On the other hand, nonpredatory clients present a lower cost for cheating, and thus experience more cheating behaviors from the cleaners. Some evidence suggest that physiological processes can mediate the cleaners' decision to switch from cooperating to cheating in mutualistic interactions. For example, in the bluestreak cleaner wrasse, changes in cortisol levels are associated with behavior changes. For smaller clients, increase cortisol levels in the water lead to more cooperative behavior, while for larger clients, the same treatment lead to more dishonest behavior. It has been suggested that "good behavior" toward smaller clients often allow wrasses to attract larger clients that are often cheated.

Other

Other models of cheating include the European tree frog, "Hyla arborea". In many sexually reproducing species such as this, some males can access mates by exploiting resources of more competitive males. Many species have dynamic reproductive strategies that can change in response to changes in the environment. In these instances, several factors contribute to the decision to switch between mating strategies. For example, in the European tree frog, a sexually competitive (as in, perceived to be attractive by females) male tend to call to attract mates. This is often referred to as the "bourgeois" tactic. On the other hand, a smaller male that would likely fail to attract mates using the bourgeois tactic will tend to hide near attractive males and attempt to access females. In this instance, the males can gain access to females without having to defend territories or acquiring additional resources (which often serve as the basis for attractiveness). This is referred to as the "parasitic" tactic, where the smaller male effectively cheats its way to accessing females, by reaping the benefit of sexual reproduction without contributing resources that normally attract females. Models such as this provide valuable tools for research aimed at energetic constraints and environmental cues involved in cheating. Studies find that mating strategies are highly adaptable and depend on a variety of factors, such as competitiveness, energetic costs involved in defending territory or acquiring resources.

Constraints and countermeasures

Environmental conditions and social interactions affecting microbial cheating

Like many other organisms, bacteria rely on iron intake for its biological processes. However, iron is sometimes difficult to access in certain environments, like soil. Some bacteria have evolved siderophores, iron-chelating particles that seek and bring back iron for the bacteria. Siderophores are not necessarily specific to its producer - sometimes another individual could take up the particles instead. Pseudomonas fluorescens is a bacterium commonly found in the soil. Under low-iron conditions, P. fluorescens produces siderophores, specifically pyoverdine, to retrieve the iron necessary for survival. However, when iron is readily available, either from freely diffusing in environment or another bacterium's siderophores, P. fluorescens ceases production, allowing the bacterium to devote its energy towards growth. One study showed that when P. fluorescens grew in association with Streptomyces ambofaciens, another bacterium that produces the siderophore coelichen, no pyoverdine was detected. This result suggested that P. fluorescens ceased siderophore production in favor of taking up iron-bound coelichen, an association also known as siderophore piracy.

More studies, however, suggested that P. fluorescens' cheating behavior could be suppressed. In another study, two strains of P. fluorescens were studied in the soil, their natural environment. One strain, known as the producer, produced a higher level of siderophores, which meant that other strain, known as the non-producer, ceased siderophore production in favor of using the other's siderophores. Although one would expect that the non-producer would outcompete the producer, like the P. fluorescens and S. ambofaciens association, the study demonstrated that the non-producer was unable to do so in soil conditions, suggesting that the two strains could coexist. Further experiments suggested that this cheating prevention may be due to interactions with other microbes in the soil influencing the relationship or the spatial structure of the soil preventing siderophore diffusion and therefore limiting the non-producer's ability to exploit the producer's siderophores.

Selection pressure in bacteria (intraspecies)

By definition, individuals cheat to gain benefits that their non-cheating counterparts do not receive. How then can a cooperative system exist in face of these cheaters? One answer is that the cheaters actually have a reduced fitness compared to the non-cheaters. In a study by Dandekar et al., the researchers examined the survival rates of cheating and non-cheating bacteria populations (Pseudomonas aeruginosa) under varying environmental conditions. These microorganisms, like many species of bacteria, use a cell-cell communication system called quorum sensing that detect their population density and prompt the transcription of various resources when needed. In this case, the resources are publicly shared proteases that break down a food source like casein, and privately used adenosine hydrolase, which breaks down another food source, adenosine. The problem arises when some individuals ("cheaters") do not respond to these quorum sensing signals and therefore do not contribute to the costly protease production yet enjoys the benefits of the broken down resources.

When P. aeruginosa populations are placed into growth conditions where cooperation (and responding to the quorum signal) is costly, the number of cheaters increases, and the public resources are depleted, which can lead to a tragedy of the commons. However, when P. aeruginosa populations are placed into growth conditions with a proportion of adenosine, the cheaters are suppressed because the bacteria that responds to the quorum signal now produces adenosine hydrolase that they privately use for themselves to digest adenosine food source. In wild populations where the presence of adenosine is common, this is an explanation for how individuals that cooperate could have higher fitness than those that cheat, thereby suppressing the cheaters and maintaining cooperation.

Policing/punishment in insects

Cheating is also commonly found in insects. The social and seemingly altruistic communities found in insects such as ants and bees provide ample opportunities for cheaters to take advantage of the system and accrue additional benefits at the expense of the community.

Wasp nest, with some larvae

Sometimes, a colony of insects is called a "superorganism" for its ability to take on properties greater than those of the sum of individuals. A colony of insects in which different individuals are specialized for specific tasks means a greater colony production and greater efficiency. Moreover, based on the kin-selection theory, it is collectively beneficial for all the individuals in the community to have the queen to lay eggs rather the workers lay eggs. This is because if the workers lay eggs, it benefits the egg-laying worker individually, but the rest of the workers are now twice removed from this worker's offspring. Therefore, though it is beneficial for one individual to have its own offspring, it is collectively beneficial to have the queen lay the eggs. Therefore, a system of worker and queen policing exists against worker-laid eggs.

One form of policing occurs by the oophagy of the worker-laid eggs, found in many ant and bee species. This could be done by both or either the queen or the workers. In a series of experiments with honeybees (Apis mellifera), Ratneiks & Visscher found that other workers effectively removed worker-laid eggs in all colonies, whether the eggs were from originated from the same colonies or not. An example of a combination of queen and worker policing is found in ants, in the genus Diacamma, in which worker-laid eggs are taken by other workers and fed to the "queen". In general, these signals that identify the eggs as queen-laid are likely incorruptible, since it must be an honest signal to be maintained and not be used by cheating workers.

The other form of policing occurs through aggression towards egg-laying workers. In a species of tree wasp Dolichovespula sylvestris, Wenseleers et al. found that a combination of aggressive behavior and destruction of worker-laid eggs kept the number of worker-laid eggs low. In fact, 91% of the worker-laid eggs were policed within one day. They also found that about 20% of workers laying eggs were prevented from doing so through both the queen's and workers' aggressive behavior. The workers and the queen would grab the egg-laying worker and try to sting her or push her off the cell. This usually results in the worker removing her abdomen and not depositing her eggs.

Policing/punishment in other organisms

A nest of naked mole rats

Aggression and punishment are not just found in insects. For example, in naked mole rats, punishments by the queen are a way she motivates the lazier, less-related workers in their groups. The queen would shove the lazier workers, with the number of shoves increasing when there are fewer active workers. Reeve found that if the queen is removed when colonies are satiated, there is a significant drop in weight of the active workers because the lazier workers are taking advantage of the system.

Punishment is also a method used by cichlid Neolamprologous pulcher in their cooperative breeding systems. It is a pay-to-stay system where helper fish are allowed to stay in certain territories in exchange for their help. Similar to the naked mole rats, the helpers that were prevented from helping, the "idle helpers", receive more aggression than control helpers in the study. Researchers theorize that this system developed because the fish are usually not closely related (so kinship benefits have little impact), and because there is a high level of predation risk when the fish is outside the group (therefore a strong motivator for the helper fish to stay in the group).

Rhesus monkeys also use aggression as a punishment. These animals have five distinct calls that they can "decide" to produce upon finding food. Whether they call or not are related to their gender and number of kins: females call more often and females with more kins call more often. However, sometimes when food is found, the individual ("discoverer") do not call to attract the kins and presumably to share food. If lower ranked individuals find this discoverer to be in the food drop area of the experiment, they recruit coalition support against this individual by screaming. The formed coalition then chases this individual away. If higher ranked individuals find this discoverer, they either chase the discoverer away or became physically aggressive towards the individual. These results show that aggression as punishment is a way to encourage members to work together and share food when it is found.

Interspecific countermeasures

Cheating and constraints of cheating are not limited to intraspecific interactions; it can also occur in a mutualistic relationship between two species. A common example is the mutualistic relationship between cleaner fish Labroides dimidiatus and reef fish. Bshary and Grutter found that cleaner wrasse prefers the client tissue mucus over ectoparasites. This creates a conflict between the cleaner fish and reef fish, because the reef fish only benefit when the cleaner fish eats the ectoparasites. Further studies revealed that in a lab setting, the cleaner fish undergoes behavioral change in face of deterrents against eating their preferential food. In several trials, the plate of their preferential food source was immediately removed when they eat it, to mimic "client fleeing" in natural settings. In other trials, the plate of their preferential food source chased the cleaner fish when they eat it, mimicking "client chasing" in natural setting. After only six learning trials, the cleaners learned to choose against their preference, indicating that punishment is potentially a very effective countermeasure against cheating in mutualistic relationships.

Nitrogen-fixing nodules in legumes

Finally the countermeasures are not limited to organismal relationships. West et al. found a similar countermeasure against cheating in legume-rhizobium mutualism. In this relationship, nitrogen fixing bacteria rhizobium fixes atmospheric N2 from inside the roots of leguminous plants, providing this essential source of nitrogen to these plants while also receiving organic acids for themselves. However, some bacteria are more mutualistic, while others are more parasitic because they consume the plant's resources but fixes little to no N2. Moreover, these plants cannot tell whether the bacteria are more or less parasitic until they are settled in the plant nodules. To prevent cheating, these plants seem to be able to punish the rhizobium bacteria. In a series of experiments, researchers forced non-cooperation between the bacteria and the plants by placing various nodules in nitrogen-free atmosphere. They saw a decrease in the rhizobium reproductive success by 50%. West et al. created a model for legume sanctioning the bacteria and hypothesizes that these behaviors exist to stabilize mutualistic interactions.

Another well-known example of plant-organism interaction occurs between yuccas and yucca moths. The female yucca moths deposit their eggs one at a time to the yucca flower. At the same time, she also deposits a small amount of pollen from yucca flowers as nutrition for the yucca moths. Because most of the pollen is not consumed by the larva, yucca moths are therefore also the active pollinators for the yucca plant. Moreover, sometimes the female moths do not successfully deposit their eggs the first time, and may try again and again. The yucca plant receives scars from the multiple attempts, but they also receive more pollen, since the moths are depositing pollen with every try.

"Cheating" sometimes happens when the yucca moth deposits too many eggs in one plant. In this case, the yucca plant has little to no benefits from this interaction. However, the plant has a unique way of constraining this behavior. While the constraint against cheating often occurs directly to the individual, in this case, the constraint occurs to the individual's offspring. The yucca plant can "abort" the moths by aborting the flowers. Pellmyr and Huth found that there is selective maturation for flowers that have low egg loads and high number of scars (and therefore a high amount of pollen). In this way, there is selection against the "cheaters" who try to use the yucca plant without providing the benefits of pollination.

Game theory

From Wikipedia, the free encyclopedia

Game theory is the study of mathematical models of strategic interaction between rational decision-makers. It has applications in all fields of social science, as well as in logic and computer science. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by the 1944 book Theory of Games and Economic Behavior, co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

Game theory was developed extensively in the 1950s by many scholars. It was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. As of 2014, with the Nobel Memorial Prize in Economic Sciences going to game theorist Jean Tirole, eleven game theorists have won the economics Nobel Prize. John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.

History

John von Neumann

John Nash

Early discussions of examples of two-person games occurred long before the rise of modern, mathematical game theory. The first known discussion of game theory occurred in a letter written by Charles Waldegrave, an active Jacobite, and uncle to James Waldegrave, a British diplomat, in 1713.^[2] In this letter, Waldegrave provides a minimax mixed strategy solution to a two-person version of the card game le Her, and the problem is now known as Waldegrave problem. James Madison made what we now recognize as a game-theoretic analysis of the ways states can be expected to behave under different systems of taxation. In his 1838 Recherches sur les principes mathématiques de la théorie des richesses (Researches into the Mathematical Principles of the Theory of Wealth), Antoine Augustin Cournot considered a duopoly and presents a solution that is a restricted version of the Nash equilibrium.

In 1913, Ernst Zermelo published Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels (On an Application of Set Theory to the Theory of the Game of Chess). It proved that the optimal chess strategy is strictly determined. This paved the way for more general theorems.

In 1938, the Danish mathematical economist Frederik Zeuthen proved that the mathematical model had a winning strategy by using Brouwer's fixed point theorem. In his 1938 book Applications aux Jeux de Hasard and earlier notes, Émile Borel proved a minimax theorem for two-person zero-sum matrix games only when the pay-off matrix was symmetric. Borel conjectured that non-existence of mixed-strategy equilibria in two-person zero-sum games would occur, a conjecture that was proved false.

Game theory did not really exist as a unique field until John von Neumann published the paper On the Theory of Games of Strategy in 1928. Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by his 1944 book Theory of Games and Economic Behavior co-authored with Oskar Morgenstern. The second edition of this book provided an axiomatic theory of utility, which reincarnated Daniel Bernoulli's old theory of utility (of the money) as an independent discipline. Von Neumann's work in game theory culminated in this 1944 book. This foundational work contains the method for finding mutually consistent solutions for two-person zero-sum games. During the following time period, work on game theory was primarily focused on cooperative game theory, which analyzes optimal strategies for groups of individuals, presuming that they can enforce agreements between them about proper strategies.

In 1950, the first mathematical discussion of the prisoner's dilemma appeared, and an experiment was undertaken by notable mathematicians Merrill M. Flood and Melvin Dresher, as part of the RAND Corporation's investigations into game theory. RAND pursued the studies because of possible applications to global nuclear strategy. Around this same time, John Nash developed a criterion for mutual consistency of players' strategies, known as Nash equilibrium, applicable to a wider variety of games than the criterion proposed by von Neumann and Morgenstern. Nash proved that every n-player, non-zero-sum (not just 2-player zero-sum) non-cooperative game has what is now known as a Nash equilibrium.

Game theory experienced a flurry of activity in the 1950s, during which time the concepts of the core, the extensive form game, fictitious play, repeated games, and the Shapley value were developed. In addition, the first applications of game theory to philosophy and political science occurred during this time.

In 1979 Robert Axelrod tried setting up computer programs as players and found that in tournaments between them the winner was often a simple "tit-for-tat" program that cooperates on the first step, then on subsequent steps just does whatever its opponent did on the previous step. The same winner was also often obtained by natural selection; a fact widely taken to explain cooperation phenomena in evolutionary biology and the social sciences.

Prize-winning achievements

In 1965, Reinhard Selten introduced his solution concept of subgame perfect equilibria, which further refined the Nash equilibrium (later he would introduce trembling hand perfection as well). In 1994 Nash, Selten and Harsanyi became Economics Nobel Laureates for their contributions to economic game theory.

In the 1970s, game theory was extensively applied in biology, largely as a result of the work of John Maynard Smith and his evolutionarily stable strategy. In addition, the concepts of correlated equilibrium, trembling hand perfection, and common knowledge were introduced and analyzed.

In 2005, game theorists Thomas Schelling and Robert Aumann followed Nash, Selten and Harsanyi as Nobel Laureates. Schelling worked on dynamic models, early examples of evolutionary game theory. Aumann contributed more to the equilibrium school, introducing an equilibrium coarsening, correlated equilibrium, and developing an extensive formal analysis of the assumption of common knowledge and of its consequences.

In 2007, Leonid Hurwicz, together with Eric Maskin and Roger Myerson, was awarded the Nobel Prize in Economics "for having laid the foundations of mechanism design theory". Myerson's contributions include the notion of proper equilibrium, and an important graduate text: Game Theory, Analysis of Conflict. Hurwicz introduced and formalized the concept of incentive compatibility.

In 2012, Alvin E. Roth and Lloyd S. Shapley were awarded the Nobel Prize in Economics "for the theory of stable allocations and the practice of market design" and, in 2014, the Nobel went to game theorist Jean Tirole.

Game types

Cooperative / Non-cooperative

A game is cooperative if the players are able to form binding commitments externally enforced (e.g. through contract law). A game is non-cooperative if players cannot form alliances or if all agreements need to be self-enforcing (e.g. through credible threats).

Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria.

Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will affect the distribution of payoffs within each coalition. As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory (the converse does not hold) provided that sufficient assumptions are made to encompass all the possible strategies available to players due to the possibility of external enforcement of cooperation. While it would thus be optimal to have all games expressed under a non-cooperative framework, in many instances insufficient information is available to accurately model the formal procedures available to the players during the strategic bargaining process, or the resulting model would be of too high complexity to offer a practical tool in the real world. In such cases, cooperative game theory provides a simplified approach that allows analysis of the game at large without having to make any assumption about bargaining powers.

Symmetric / Asymmetric

	E	F
E	1, 2	0, 0
F	0, 0	1, 2
An asymmetric game

A symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If the identities of the players can be changed without changing the payoff to the strategies, then a game is symmetric. Many of the commonly studied 2×2 games are symmetric. The standard representations of chicken, the prisoner's dilemma, and the stag hunt are all symmetric games. Some scholars would consider certain asymmetric games as examples of these games as well. However, the most common payoffs for each of these games are symmetric. Most commonly studied asymmetric games are games where there are not identical strategy sets for both players. For instance, the ultimatum game and similarly the dictator game have different strategies for each player. It is possible, however, for a game to have identical strategies for both players, yet be asymmetric. For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players.

Zero-sum / Non-zero-sum

	A	B
A	–1, 1	3, –3
B	0, 0	–2, 2
A zero-sum game

Zero-sum games are a special case of constant-sum games, in which choices by players can neither increase nor decrease the available resources. In zero-sum games the total benefit to all players in the game, for every combination of strategies, always adds to zero (more informally, a player benefits only at the equal expense of others). Poker exemplifies a zero-sum game (ignoring the possibility of the house's cut), because one wins exactly the amount one's opponents lose. Other zero-sum games include matching pennies and most classical board games including Go and chess.

Many games studied by game theorists (including the famed prisoner's dilemma) are non-zero-sum games, because the outcome has net results greater or less than zero. Informally, in non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another.

Constant-sum games correspond to activities like theft and gambling, but not to the fundamental economic situation in which there are potential gains from trade. It is possible to transform any game into a (possibly asymmetric) zero-sum game by adding a dummy player (often called "the board") whose losses compensate the players' net winnings.

Simultaneous / Sequential

Simultaneous games are games where both players move simultaneously, or if they do not move simultaneously, the later players are unaware of the earlier players' actions (making them effectively simultaneous). Sequential games (or dynamic games) are games where later players have some knowledge about earlier actions. This need not be perfect information about every action of earlier players; it might be very little knowledge. For instance, a player may know that an earlier player did not perform one particular action, while s/he does not know which of the other available actions the first player actually performed.

The difference between simultaneous and sequential games is captured in the different representations discussed above. Often, normal form is used to represent simultaneous games, while extensive form is used to represent sequential ones. The transformation of extensive to normal form is one way, meaning that multiple extensive form games correspond to the same normal form. Consequently, notions of equilibrium for simultaneous games are insufficient for reasoning about sequential games; see subgame perfection.

In short, the differences between sequential and simultaneous games are as follows:

	Sequential	Simultaneous
Normally denoted by	Decision trees	Payoff matrices
Prior knowledge of opponent's move?	Yes	No
Time axis?	Yes	No
Also known as	Extensive-form game Extensive game	Strategy game Strategic game

Perfect information and imperfect information

A game of imperfect information (the dotted line represents ignorance on the part of player 2, formally called an information set)

An important subset of sequential games consists of games of perfect information. A game is one of perfect information if all players know the moves previously made by all other players. Most games studied in game theory are imperfect-information games. Examples of perfect-information games include tic-tac-toe, checkers, infinite chess, and Go.

Many card games are games of imperfect information, such as poker and bridge. Perfect information is often confused with complete information, which is a similar concept. Complete information requires that every player know the strategies and payoffs available to the other players but not necessarily the actions taken. Games of incomplete information can be reduced, however, to games of imperfect information by introducing "moves by nature".

Combinatorial games

Games in which the difficulty of finding an optimal strategy stems from the multiplicity of possible moves are called combinatorial games. Examples include chess and go. Games that involve imperfect information may also have a strong combinatorial character, for instance backgammon. There is no unified theory addressing combinatorial elements in games. There are, however, mathematical tools that can solve particular problems and answer general questions.

Games of perfect information have been studied in combinatorial game theory, which has developed novel representations, e.g. surreal numbers, as well as combinatorial and algebraic (and sometimes non-constructive) proof methods to solve games of certain types, including "loopy" games that may result in infinitely long sequences of moves. These methods address games with higher combinatorial complexity than those usually considered in traditional (or "economic") game theory. A typical game that has been solved this way is hex. A related field of study, drawing from computational complexity theory, is game complexity, which is concerned with estimating the computational difficulty of finding optimal strategies.

Research in artificial intelligence has addressed both perfect and imperfect information games that have very complex combinatorial structures (like chess, go, or backgammon) for which no provable optimal strategies have been found. The practical solutions involve computational heuristics, like alpha-beta pruning or use of artificial neural networks trained by reinforcement learning, which make games more tractable in computing practice.

Infinitely long games

Games, as studied by economists and real-world game players, are generally finished in finitely many moves. Pure mathematicians are not so constrained, and set theorists in particular study games that last for infinitely many moves, with the winner (or other payoff) not known until after all those moves are completed.

The focus of attention is usually not so much on the best way to play such a game, but whether one player has a winning strategy. (It can be proven, using the axiom of choice, that there are games – even with perfect information and where the only outcomes are "win" or "lose" – for which neither player has a winning strategy.) The existence of such strategies, for cleverly designed games, has important consequences in descriptive set theory.

Discrete and continuous games

Much of game theory is concerned with finite, discrete games, that have a finite number of players, moves, events, outcomes, etc. Many concepts can be extended, however. Continuous games allow players to choose a strategy from a continuous strategy set. For instance, Cournot competition is typically modeled with players' strategies being any non-negative quantities, including fractional quantities.

Differential games

Differential games such as the continuous pursuit and evasion game are continuous games where the evolution of the players' state variables is governed by differential equations. The problem of finding an optimal strategy in a differential game is closely related to the optimal control theory. In particular, there are two types of strategies: the open-loop strategies are found using the Pontryagin maximum principle while the closed-loop strategies are found using Bellman's Dynamic Programming method.
A particular case of differential games are the games with a random time horizon. In such games, the terminal time is a random variable with a given probability distribution function. Therefore, the players maximize the mathematical expectation of the cost function. It was shown that the modified optimization problem can be reformulated as a discounted differential game over an infinite time interval.

Evolutionary game theory

Evolutionary game theory studies players who adjust their strategies over time according to rules that are not necessarily rational or farsighted. In general, the evolution of strategies over time according to such rules is modeled as a Markov chain with a state variable such as the current strategy profile or how the game has been played in the recent past. Such rules may feature imitation, optimization or survival of the fittest.

In biology, such models can represent (biological) evolution, in which offspring adopt their parents' strategies and parents who play more successful strategies (i.e. corresponding to higher payoffs) have a greater number of offspring. In the social sciences, such models typically represent strategic adjustment by players who play a game many times within their lifetime and, consciously or unconsciously, occasionally adjust their strategies.

Stochastic outcomes (and relation to other fields)

Individual decision problems with stochastic outcomes are sometimes considered "one-player games". These situations are not considered game theoretical by some authors. They may be modeled using similar tools within the related disciplines of decision theory, operations research, and areas of artificial intelligence, particularly AI planning (with uncertainty) and multi-agent system. Although these fields may have different motivators, the mathematics involved are substantially the same, e.g. using Markov decision processes (MDP).

Stochastic outcomes can also be modeled in terms of game theory by adding a randomly acting player who makes "chance moves" ("moves by nature"). This player is not typically considered a third player in what is otherwise a two-player game, but merely serves to provide a roll of the dice where required by the game.

For some problems, different approaches to modeling stochastic outcomes may lead to different solutions. For example, the difference in approach between MDPs and the minimax solution is that the latter considers the worst-case over a set of adversarial moves, rather than reasoning in expectation about these moves given a fixed probability distribution. The minimax approach may be advantageous where stochastic models of uncertainty are not available, but may also be overestimating extremely unlikely (but costly) events, dramatically swaying the strategy in such scenarios if it is assumed that an adversary can force such an event to happen.

General models that include all elements of stochastic outcomes, adversaries, and partial or noisy observability (of moves by other players) have also been studied. The "gold standard" is considered to be partially observable stochastic game (POSG), but few realistic problems are computationally feasible in POSG representation.

Metagames

These are games the play of which is the development of the rules for another game, the target or subject game. Metagames seek to maximize the utility value of the rule set developed. The theory of metagames is related to mechanism design theory.

The term metagame analysis is also used to refer to a practical approach developed by Nigel Howard. whereby a situation is framed as a strategic game in which stakeholders try to realise their objectives by means of the options available to them. Subsequent developments have led to the formulation of confrontation analysis.

Pooling games

These are games prevailing over all forms of society. Pooling games are repeated plays with changing payoff table in general over an experienced path and their equilibrium strategies usually take a form of evolutionary social convention and economic convention. Pooling game theory emerges to formally recognize the interaction between optimal choice in one play and the emergence of forthcoming payoff table update path, identify the invariance existence and robustness, and predict variance over time. The theory is based upon topological transformation classification of payoff table update over time to predict variance and invariance, and is also within the jurisdiction of the computational law of reachable optimality for ordered system.

Mean field game theory

Mean field game theory is the study of strategic decision making in very large populations of small interacting agents. This class of problems was considered in the economics literature by Boyan Jovanovic and Robert W. Rosenthal, in the engineering literature by Peter E. Caines and by mathematician Pierre-Louis Lions and Jean-Michel Lasry.

Representation of games

The games studied in game theory are well-defined mathematical objects. To be fully defined, a game must specify the following elements: the players of the game, the information and actions available to each player at each decision point, and the payoffs for each outcome. (Eric Rasmusen refers to these four "essential elements" by the acronym "PAPI".) A game theorist typically uses these elements, along with a solution concept of their choosing, to deduce a set of equilibrium strategies for each player such that, when these strategies are employed, no player can profit by unilaterally deviating from their strategy. These equilibrium strategies determine an equilibrium to the game—a stable state in which either one outcome occurs or a set of outcomes occur with known probability. Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games.

Extensive form

An extensive form game

The extensive form can be used to formalize games with a time sequencing of moves. Games here are played on trees (as pictured here). Here each vertex (or node) represents a point of choice for a player. The player is specified by a number listed by the vertex. The lines out of the vertex represent a possible action for that player. The payoffs are specified at the bottom of the tree. The extensive form can be viewed as a multi-player generalization of a decision tree. To solve any extensive form game, backward induction must be used. It involves working backwards up the game tree to determine what a rational player would do at the last vertex of the tree, what the player with the previous move would do given that the player with the last move is rational, and so on until the first vertex of the tree is reached.

The game pictured consists of two players. The way this particular game is structured (i.e., with sequential decision making and perfect information), Player 1 "moves" first by choosing either F or U (Fair or Unfair). Next in the sequence, Player 2, who has now seen Player 1's move, chooses to play either A or R. Once Player 2 has made his/ her choice, the game is considered finished and each player gets their respective payoff. Suppose that Player 1 chooses U and then Player 2 chooses A: Player 1 then gets a payoff of "eight" (which in real-world terms can be interpreted in many ways, the simplest of which is in terms of money but could mean things such as eight days of vacation or eight countries conquered or even eight more opportunities to play the same game against other players) and Player 2 gets a payoff of "two".

The extensive form can also capture simultaneous-move games and games with imperfect information. To represent it, either a dotted line connects different vertices to represent them as being part of the same information set (i.e. the players do not know at which point they are), or a closed line is drawn around them. (See example in the imperfect information section.)

Normal form

	Player 2 chooses Left	Player 2 chooses Right
Player 1 chooses Up	4, 3	–1, –1
Player 1 chooses Down	0, 0	3, 4
Normal form or payoff matrix of a 2-player, 2-strategy game

The normal (or strategic form) game is usually represented by a matrix which shows the players, strategies, and payoffs (see the example to the right). More generally it can be represented by any function that associates a payoff for each player with every possible combination of actions. In the accompanying example there are two players; one chooses the row and the other chooses the column. Each player has two strategies, which are specified by the number of rows and the number of columns. The payoffs are provided in the interior. The first number is the payoff received by the row player (Player 1 in our example); the second is the payoff for the column player (Player 2 in our example). Suppose that Player 1 plays Up and that Player 2 plays Left. Then Player 1 gets a payoff of 4, and Player 2 gets 3.

When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other. If players have some information about the choices of other players, the game is usually presented in extensive form.

Every extensive-form game has an equivalent normal-form game, however the transformation to normal form may result in an exponential blowup in the size of the representation, making it computationally impractical.

Characteristic function form

In games that possess removable utility, separate rewards are not given; rather, the characteristic function decides the payoff of each unity. The idea is that the unity that is 'empty', so to speak, does not receive a reward at all.

The origin of this form is to be found in John von Neumann and Oskar Morgenstern's book; when looking at these instances, they guessed that when a union ${\displaystyle \mathbf {C} }$ appears, it works against the fraction ${\displaystyle \left({\frac {\mathbf {N} }{\mathbf {C} }}\right)}$ as if two individuals were playing a normal game. The balanced payoff of C is a basic function. Although there are differing examples that help determine coalitional amounts from normal games, not all appear that in their function form can be derived from such.

Formally, a characteristic function is seen as: (N,v), where N represents the group of people and ${\displaystyle v:2^{N}\to \mathbf {R} }$ is a normal utility.

Such characteristic functions have expanded to describe games where there is no removable utility.

General and applied uses

As a method of applied mathematics, game theory has been used to study a wide variety of human and animal behaviors. It was initially developed in economics to understand a large collection of economic behaviors, including behaviors of firms, markets, and consumers. The first use of game-theoretic analysis was by Antoine Augustin Cournot in 1838 with his solution of the Cournot duopoly. The use of game theory in the social sciences has expanded, and game theory has been applied to political, sociological, and psychological behaviors as well.

Although pre-twentieth century naturalists such as Charles Darwin made game-theoretic kinds of statements, the use of game-theoretic analysis in biology began with Ronald Fisher's studies of animal behavior during the 1930s. This work predates the name "game theory", but it shares many important features with this field. The developments in economics were later applied to biology largely by John Maynard Smith in his book Evolution and the Theory of Games.

In addition to being used to describe, predict, and explain behavior, game theory has also been used to develop theories of ethical or normative behavior and to prescribe such behavior. In economics and philosophy, scholars have applied game theory to help in the understanding of good or proper behavior. Game-theoretic arguments of this type can be found as far back as Plato.

Description and modeling

A four-stage centipede game

The primary use of game theory is to describe and model how human populations behave. Some scholars believe that by finding the equilibria of games they can predict how actual human populations will behave when confronted with situations analogous to the game being studied. This particular view of game theory has been criticized. It is argued that the assumptions made by game theorists are often violated when applied to real world situations. Game theorists usually assume players act rationally, but in practice, human behavior often deviates from this model. Game theorists respond by comparing their assumptions to those used in physics. Thus while their assumptions do not always hold, they can treat game theory as a reasonable scientific ideal akin to the models used by physicists. However, empirical work has shown that in some classic games, such as the centipede game, guess 2/3 of the average game, and the dictator game, people regularly do not play Nash equilibria. There is an ongoing debate regarding the importance of these experiments and whether the analysis of the experiments fully captures all aspects of the relevant situation.

Some game theorists, following the work of John Maynard Smith and George R. Price, have turned to evolutionary game theory in order to resolve these issues. These models presume either no rationality or bounded rationality on the part of players. Despite the name, evolutionary game theory does not necessarily presume natural selection in the biological sense. Evolutionary game theory includes both biological as well as cultural evolution and also models of individual learning (for example, fictitious play dynamics).

Prescriptive or normative analysis

	Cooperate	Defect
Cooperate	-1, -1	-10, 0
Defect	0, -10	-5, -5
The Prisoner's Dilemma

Some scholars, like Leonard Savage, see game theory not as a predictive tool for the behavior of human beings, but as a suggestion for how people ought to behave. Since a strategy, corresponding to a Nash equilibrium of a game constitutes one's best response to the actions of the other players – provided they are in (the same) Nash equilibrium – playing a strategy that is part of a Nash equilibrium seems appropriate. This normative use of game theory has also come under criticism.

Economics and business

Game theory is a major method used in mathematical economics and business for modeling competing behaviors of interacting agents. Applications include a wide array of economic phenomena and approaches, such as auctions, bargaining, mergers & acquisitions pricing, fair division, duopolies, oligopolies, social network formation, agent-based computational economics, general equilibrium, mechanism design, and voting systems; and across such broad areas as experimental economics, behavioral economics, information economics, industrial organization, and political economy.

This research usually focuses on particular sets of strategies known as "solution concepts" or "equilibria". A common assumption is that players act rationally. In non-cooperative games, the most famous of these is the Nash equilibrium. A set of strategies is a Nash equilibrium if each represents a best response to the other strategies. If all the players are playing the strategies in a Nash equilibrium, they have no unilateral incentive to deviate, since their strategy is the best they can do given what others are doing.

The payoffs of the game are generally taken to represent the utility of individual players.
A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of a particular economic situation. One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type. Naturally one might wonder to what use this information should be put. Economists and business professors suggest two primary uses (noted above): descriptive and prescriptive.

Political science

The application of game theory to political science is focused in the overlapping areas of fair division, political economy, public choice, war bargaining, positive political theory, and social choice theory. In each of these areas, researchers have developed game-theoretic models in which the players are often voters, states, special interest groups, and politicians.

Early examples of game theory applied to political science are provided by Anthony Downs. In his book An Economic Theory of Democracy, he applies the Hotelling firm location model to the political process. In the Downsian model, political candidates commit to ideologies on a one-dimensional policy space. Downs first shows how the political candidates will converge to the ideology preferred by the median voter if voters are fully informed, but then argues that voters choose to remain rationally ignorant which allows for candidate divergence. Game Theory was applied in 1962 to the Cuban missile crisis during the presidency of John F. Kennedy.

It has also been proposed that game theory explains the stability of any form of political government. Taking the simplest case of a monarchy, for example, the king, being only one person, does not and cannot maintain his authority by personally exercising physical control over all or even any significant number of his subjects. Sovereign control is instead explained by the recognition by each citizen that all other citizens expect each other to view the king (or other established government) as the person whose orders will be followed. Coordinating communication among citizens to replace the sovereign is effectively barred, since conspiracy to replace the sovereign is generally punishable as a crime. Thus, in a process that can be modeled by variants of the prisoner's dilemma, during periods of stability no citizen will find it rational to move to replace the sovereign, even if all the citizens know they would be better off if they were all to act collectively.

A game-theoretic explanation for democratic peace is that public and open debate in democracies send clear and reliable information regarding their intentions to other states. In contrast, it is difficult to know the intentions of nondemocratic leaders, what effect concessions will have, and if promises will be kept. Thus there will be mistrust and unwillingness to make concessions if at least one of the parties in a dispute is a non-democracy.

On the other hand, game theory predicts that two countries may still go to war even if their leaders are cognizant of the costs of fighting. War may result from asymmetric information; two countries may have incentives to mis-represent the amount of military resources they have on hand, rendering them unable to settle disputes agreeably without resorting to fighting. Moreover, war may arise because of commitment problems: if two countries wish to settle a dispute via peaceful means, but each wishes to go back on the terms of that settlement, they may have no choice but to resort to warfare. Finally, war may result from issue indivisibilities.

Game theory could also help predict a nation's responses when there is a new rule or law to be applied to that nation. One example would be Peter John Wood's (2013) research when he looked into what nations could do to help reduce climate change. Wood thought this could be accomplished by making treaties with other nations to reduce green house gas emissions. However, he concluded that this idea could not work because it would create a prisoner's dilemma to the nations.

Biology

	Hawk	Dove
Hawk	20, 20	80, 40
Dove	40, 80	60, 60
The hawk-dove game

Unlike those in economics, the payoffs for games in biology are often interpreted as corresponding to fitness. In addition, the focus has been less on equilibria that correspond to a notion of rationality and more on ones that would be maintained by evolutionary forces. The best known equilibrium in biology is known as the evolutionarily stable strategy (ESS), first introduced in (Smith & Price 1973). Although its initial motivation did not involve any of the mental requirements of the Nash equilibrium, every ESS is a Nash equilibrium.

In biology, game theory has been used as a model to understand many different phenomena. It was first used to explain the evolution (and stability) of the approximate 1:1 sex ratios. (Fisher 1930) suggested that the 1:1 sex ratios are a result of evolutionary forces acting on individuals who could be seen as trying to maximize their number of grandchildren.

Additionally, biologists have used evolutionary game theory and the ESS to explain the emergence of animal communication. The analysis of signaling games and other communication games has provided insight into the evolution of communication among animals. For example, the mobbing behavior of many species, in which a large number of prey animals attack a larger predator, seems to be an example of spontaneous emergent organization. Ants have also been shown to exhibit feed-forward behavior akin to fashion.

Biologists have used the game of chicken to analyze fighting behavior and territoriality.

According to Maynard Smith, in the preface to Evolution and the Theory of Games, "paradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed". Evolutionary game theory has been used to explain many seemingly incongruous phenomena in nature.

One such phenomenon is known as biological altruism. This is a situation in which an organism appears to act in a way that benefits other organisms and is detrimental to itself. This is distinct from traditional notions of altruism because such actions are not conscious, but appear to be evolutionary adaptations to increase overall fitness. Examples can be found in species ranging from vampire bats that regurgitate blood they have obtained from a night's hunting and give it to group members who have failed to feed, to worker bees that care for the queen bee for their entire lives and never mate, to vervet monkeys that warn group members of a predator's approach, even when it endangers that individual's chance of survival. All of these actions increase the overall fitness of a group, but occur at a cost to the individual.

Evolutionary game theory explains this altruism with the idea of kin selection. Altruists discriminate between the individuals they help and favor relatives. Hamilton's rule explains the evolutionary rationale behind this selection with the equation c < b × r, where the cost c to the altruist must be less than the benefit b to the recipient multiplied by the coefficient of relatedness r. The more closely related two organisms are causes the incidences of altruism to increase because they share many of the same alleles. This means that the altruistic individual, by ensuring that the alleles of its close relative are passed on through survival of its offspring, can forgo the option of having offspring itself because the same number of alleles are passed on. For example, helping a sibling (in diploid animals) has a coefficient of ½, because (on average) an individual shares ½ of the alleles in its sibling's offspring. Ensuring that enough of a sibling's offspring survive to adulthood precludes the necessity of the altruistic individual producing offspring. The coefficient values depend heavily on the scope of the playing field; for example if the choice of whom to favor includes all genetic living things, not just all relatives, we assume the discrepancy between all humans only accounts for approximately 1% of the diversity in the playing field, a co-efficient that was ½ in the smaller field becomes 0.995. Similarly if it is considered that information other than that of a genetic nature (e.g. epigenetics, religion, science, etc.) persisted through time the playing field becomes larger still, and the discrepancies smaller.

Computer science and logic

Game theory has come to play an increasingly important role in logic and in computer science. Several logical theories have a basis in game semantics. In addition, computer scientists have used games to model interactive computations. Also, game theory provides a theoretical basis to the field of multi-agent systems.

Separately, game theory has played a role in online algorithms; in particular, the k-server problem, which has in the past been referred to as games with moving costs and request-answer games. Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms, especially online algorithms.

The emergence of the internet has motivated the development of algorithms for finding equilibria in games, markets, computational auctions, peer-to-peer systems, and security and information markets. Algorithmic game theory and within it algorithmic mechanism design combine computational algorithm design and analysis of complex systems with economic theory.

Philosophy

	Stag	Hare
Stag	3, 3	0, 2
Hare	2, 0	2, 2
Stag hunt

Game theory has been put to several uses in philosophy. Responding to two papers by W.V.O. Quine (1960, 1967), Lewis (1969) used game theory to develop a philosophical account of convention. In so doing, he provided the first analysis of common knowledge and employed it in analyzing play in coordination games. In addition, he first suggested that one can understand meaning in terms of signaling games. This later suggestion has been pursued by several philosophers since Lewis. Following Lewis (1969) game-theoretic account of conventions, Edna Ullmann-Margalit (1977) and Bicchieri (2006) have developed theories of social norms that define them as Nash equilibria that result from transforming a mixed-motive game into a coordination game.

Game theory has also challenged philosophers to think in terms of interactive epistemology: what it means for a collective to have common beliefs or knowledge, and what are the consequences of this knowledge for the social outcomes resulting from the interactions of agents. Philosophers who have worked in this area include Bicchieri (1989, 1993), Skyrms (1990), and Stalnaker (1999).

In ethics, some (most notably David Gauthier, Gregory Kavka, and Jean Hampton) authors have attempted to pursue Thomas Hobbes' project of deriving morality from self-interest. Since games like the prisoner's dilemma present an apparent conflict between morality and self-interest, explaining why cooperation is required by self-interest is an important component of this project. This general strategy is a component of the general social contract view in political philosophy.

Other authors have attempted to use evolutionary game theory in order to explain the emergence of human attitudes about morality and corresponding animal behaviors. These authors look at several games including the prisoner's dilemma, stag hunt, and the Nash bargaining game as providing an explanation for the emergence of attitudes about morality (see, e.g., Skyrms (1996, 2004) and Sober and Wilson (1999)).

In popular culture

• Based on the 1998 book by Sylvia Nasar, the life story of game theorist and mathematician John Nash was turned into the 2001 biopic A Beautiful Mind, starring Russell Crowe as Nash.
• The 1959 military science fiction novel Starship Troopers by Robert A. Heinlein mentioned "games theory" and "theory of games". In the 1997 film of the same name, the character Carl Jenkins referred to his military intelligence assignment as being assigned to "games and theory".
• The 1964 film Dr. Strangelove satirizes game theoretic ideas about deterrence theory. For example, nuclear deterrence depends on the threat to retaliate catastrophically if a nuclear attack is detected. A game theorist might argue that such threats can fail to be credible, in the sense that they can lead to subgame imperfect equilibria. The movie takes this idea one step further, with the Russians irrevocably committing to a catastrophic nuclear response without making the threat public.
• The 1980s power pop band Game Theory was founded by singer/songwriter Scott Miller, who described the band's name as alluding to "the study of calculating the most appropriate action given an adversary... to give yourself the minimum amount of failure."
• Liar Game, a 2005 Japanese manga and 2007 television series, presents the main characters in each episode with a game or problem that is typically drawn from game theory, as demonstrated by the strategies applied by the characters.