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Friday, February 8, 2019

Evolutionarily stable strategy

From Wikipedia, the free encyclopedia

Evolutionarily stable strategy
A solution concept in game theory
Relationship
Subset ofNash equilibrium
Superset ofStochastically stable equilibrium, Stable Strong Nash equilibrium
Intersects withSubgame perfect equilibrium, Trembling hand perfect equilibrium, Perfect Bayesian equilibrium
Significance
Proposed byJohn Maynard Smith and George R. Price
Used forBiological modeling and Evolutionary game theory
ExampleHawk-dove

An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) which, if adopted by a population in a given environment, is impenetrable, meaning that it cannot be invaded by any alternative strategy (or strategies) that are initially rare. It is relevant in game theory, behavioral ecology, and evolutionary psychology. An ESS is an equilibrium refinement of the Nash equilibrium. It is a Nash equilibrium that is "evolutionarily" stable: once it is fixed in a population, natural selection alone is sufficient to prevent alternative (mutant) strategies from invading successfully. The theory is not intended to deal with the possibility of gross external changes to the environment that bring new selective forces to bear.

First published as a specific term in the 1972 book by John Maynard Smith, the ESS is widely used in behavioural ecology and economics, and has been used in anthropology, evolutionary psychology, philosophy, and political science.

History

Evolutionarily stable strategies were defined and introduced by John Maynard Smith and George R. Price in a 1973 Nature paper. Such was the time taken in peer-reviewing the paper for Nature that this was preceded by a 1972 essay by Maynard Smith in a book of essays titled On Evolution. The 1972 essay is sometimes cited instead of the 1973 paper, but university libraries are much more likely to have copies of Nature. Papers in Nature are usually short; in 1974, Maynard Smith published a longer paper in the Journal of Theoretical Biology. Maynard Smith explains further in his 1982 book Evolution and the Theory of Games. Sometimes these are cited instead. In fact, the ESS has become so central to game theory that often no citation is given, as the reader is assumed to be familiar with it. 

Maynard Smith mathematically formalized a verbal argument made by Price, which he read while peer-reviewing Price's paper. When Maynard Smith realized that the somewhat disorganized Price was not ready to revise his article for publication, he offered to add Price as co-author. 

The concept was derived from R. H. MacArthur and W. D. Hamilton's work on sex ratios, derived from Fisher's principle, especially Hamilton's (1967) concept of an unbeatable strategy. Maynard Smith was jointly awarded the 1999 Crafoord Prize for his development of the concept of evolutionarily stable strategies and the application of game theory to the evolution of behavior.
Uses of ESS:

Motivation

The Nash equilibrium is the traditional solution concept in game theory. It depends on the cognitive abilities of the players. It is assumed that players are aware of the structure of the game and consciously try to predict the moves of their opponents and to maximize their own payoffs. In addition, it is presumed that all the players know this (see common knowledge). These assumptions are then used to explain why players choose Nash equilibrium strategies.

Evolutionarily stable strategies are motivated entirely differently. Here, it is presumed that the players' strategies are biologically encoded and heritable. Individuals have no control over their strategy and need not be aware of the game. They reproduce and are subject to the forces of natural selection, with the payoffs of the game representing reproductive success (biological fitness). It is imagined that alternative strategies of the game occasionally occur, via a process like mutation. To be an ESS, a strategy must be resistant to these alternatives. 

Given the radically different motivating assumptions, it may come as a surprise that ESSes and Nash equilibria often coincide. In fact, every ESS corresponds to a Nash equilibrium, but some Nash equilibria are not ESSes.

Nash equilibrium

An ESS is a refined or modified form of a Nash equilibrium. In a Nash equilibrium, if all players adopt their respective parts, no player can benefit by switching to any alternative strategy. In a two player game, it is a strategy pair. Let E(S,T) represent the payoff for playing strategy S against strategy T. The strategy pair (S, S) is a Nash equilibrium in a two player game if and only if this is true for both players and for all TS:
E(S,S) ≥ E(T,S)
In this definition, strategy T can be a neutral alternative to S (scoring equally well, but not better). A Nash equilibrium is presumed to be stable even if T scores equally, on the assumption that there is no long-term incentive for players to adopt T instead of S. This fact represents the point of departure of the ESS. 

Maynard Smith and Price specify two conditions for a strategy S to be an ESS. For all TS, either
  1. E(S,S) > E(T,S), or
  2. E(S,S) = E(T,S) and E(S,T) > E(T,T)
The first condition is sometimes called a strict Nash equilibrium. The second is sometimes called "Maynard Smith's second condition". The second condition means that although strategy T is neutral with respect to the payoff against strategy S, the population of players who continue to play strategy S has an advantage when playing against T

There is also an alternative, stronger definition of ESS, due to Thomas. This places a different emphasis on the role of the Nash equilibrium concept in the ESS concept. Following the terminology given in the first definition above, this definition requires that for all TS
  1. E(S,S) ≥ E(T,S), and
  2. E(S,T) > E(T,T)
In this formulation, the first condition specifies that the strategy is a Nash equilibrium, and the second specifies that Maynard Smith's second condition is met. Note that the two definitions are not precisely equivalent: for example, each pure strategy in the coordination game below is an ESS by the first definition but not the second. 

In words, this definition looks like this: The payoff of the first player when both players play strategy S is higher than (or equal to) the payoff of the first player when he changes to another strategy T and the second players keeps his strategy S and the payoff of the first player when only his opponent changes his strategy to T is higher than his payoff in case that both of players change their strategies to T. 

This formulation more clearly highlights the role of the Nash equilibrium condition in the ESS. It also allows for a natural definition of related concepts such as a weak ESS or an evolutionarily stable set.

Examples of differences between Nash equilibria and ESSes

Cooperate Defect
Cooperate 3, 3 1, 4
Defect 4, 1 2, 2
Prisoner's Dilemma
A B
A 2, 2 1, 2
B 2, 1 2, 2
Harm thy neighbor

In most simple games, the ESSes and Nash equilibria coincide perfectly. For instance, in the prisoner's dilemma there is only one Nash equilibrium, and its strategy (Defect) is also an ESS.

Some games may have Nash equilibria that are not ESSes. For example, in harm thy neighbor (whose payoff matrix is shown here) both (A, A) and (B, B) are Nash equilibria, since players cannot do better by switching away from either. However, only B is an ESS (and a strong Nash). A is not an ESS, so B can neutrally invade a population of A strategists and predominate, because B scores higher against B than A does against B. This dynamic is captured by Maynard Smith's second condition, since E(A, A) = E(B, A), but it is not the case that E(A,B) > E(B,B). 


C D
C 2, 2 1, 2
D 2, 1 0, 0
Harm everyone

Swerve Stay
Swerve 0,0 −1,+1
Stay +1,−1 −20,−20
Chicken

Nash equilibria with equally scoring alternatives can be ESSes. For example, in the game Harm everyone, C is an ESS because it satisfies Maynard Smith's second condition. D strategists may temporarily invade a population of C strategists by scoring equally well against C, but they pay a price when they begin to play against each other; C scores better against D than does D. So here although E(C, C) = E(D, C), it is also the case that E(C,D) > E(D,D). As a result, C is an ESS. 

Even if a game has pure strategy Nash equilibria, it might be that none of those pure strategies are ESS. Consider the Game of chicken. There are two pure strategy Nash equilibria in this game (Swerve, Stay) and (Stay, Swerve). However, in the absence of an uncorrelated asymmetry, neither Swerve nor Stay are ESSes. There is a third Nash equilibrium, a mixed strategy which is an ESS for this game. 

This last example points to an important difference between Nash equilibria and ESS. Nash equilibria are defined on strategy sets (a specification of a strategy for each player), while ESS are defined in terms of strategies themselves. The equilibria defined by ESS must always be symmetric, and thus have fewer equilibrium points.

Vs. evolutionarily stable state

In population biology, the two concepts of an evolutionarily stable strategy (ESS) and an evolutionarily stable state are closely linked but describe different situations.

In an evolutionarily stable strategy, if all the members of a population adopt it, no mutant strategy can invade. Once virtually all members of the population use this strategy, there is no 'rational' alternative. ESS is part of classical game theory

In an evolutionarily stable state, a population's genetic composition is restored by selection after a disturbance, if the disturbance is not too large. An evolutionarily stable state is a dynamic property of a population that returns to using a strategy, or mix of strategies, if it is perturbed from that initial state. It is part of population genetics, dynamical system, or evolutionary game theory. This is now called convergent stability.

B. Thomas (1984) applies the term ESS to an individual strategy which may be mixed, and evolutionarily stable population state to a population mixture of pure strategies which may be formally equivalent to the mixed ESS.

Whether a population is evolutionarily stable does not relate to its genetic diversity: it can be genetically monomorphic or polymorphic.

Stochastic ESS

In the classic definition of an ESS, no mutant strategy can invade. In finite populations, any mutant could in principle invade, albeit at low probability, implying that no ESS can exist. In a finite population, an ESS can instead be defined as a strategy which, should it become invaded by a new mutant strategy with probability p, would be able to counterinvade from a single starting individual with probability greater than p, as illustrated by the evolution of bet-hedging.

Prisoner's dilemma


Cooperate Defect
Cooperate 3, 3 1, 4
Defect 4, 1 2, 2
Prisoner's Dilemma
A common model of altruism and social cooperation is the Prisoner's dilemma. Here a group of players would collectively be better off if they could play Cooperate, but since Defect fares better each individual player has an incentive to play Defect. One solution to this problem is to introduce the possibility of retaliation by having individuals play the game repeatedly against the same player. In the so-called iterated Prisoner's dilemma, the same two individuals play the prisoner's dilemma over and over. While the Prisoner's dilemma has only two strategies (Cooperate and Defect), the iterated Prisoner's dilemma has a huge number of possible strategies. Since an individual can have different contingency plan for each history and the game may be repeated an indefinite number of times, there may in fact be an infinite number of such contingency plans. 

Three simple contingency plans which have received substantial attention are Always Defect, Always Cooperate, and Tit for Tat. The first two strategies do the same thing regardless of the other player's actions, while the latter responds on the next round by doing what was done to it on the previous round—it responds to Cooperate with Cooperate and Defect with Defect

If the entire population plays Tit-for-Tat and a mutant arises who plays Always Defect, Tit-for-Tat will outperform Always Defect. If the population of the mutant becomes too large — the percentage of the mutant will be kept small. Tit for Tat is therefore an ESS, with respect to only these two strategies. On the other hand, an island of Always Defect players will be stable against the invasion of a few Tit-for-Tat players, but not against a large number of them. If we introduce Always Cooperate, a population of Tit-for-Tat is no longer an ESS. Since a population of Tit-for-Tat players always cooperates, the strategy Always Cooperate behaves identically in this population. As a result, a mutant who plays Always Cooperate will not be eliminated. However, even though a population of Always Cooperate and Tit-for-Tat can coexist, if there is a small percentage of the population that is Always Defect, the selective pressure is against Always Cooperate, and in favour of Tit-for-Tat. This is due to the lower payoffs of cooperating than those of defecting in case the opponent defects.

This demonstrates the difficulties in applying the formal definition of an ESS to games with large strategy spaces, and has motivated some to consider alternatives.

Human behavior

The fields of sociobiology and evolutionary psychology attempt to explain animal and human behavior and social structures, largely in terms of evolutionarily stable strategies. Sociopathy (chronic antisocial or criminal behavior) may be a result of a combination of two such strategies.

Evolutionarily stable strategies were originally considered for biological evolution, but they can apply to other contexts. In fact, there are stable states for a large class of adaptive dynamics. As a result, they can be used to explain human behaviours that lack any genetic influences.

Free-rider problem

From Wikipedia, the free encyclopedia
 
In the social sciences, the free-rider problem occurs when those who benefit from resources, public goods, or services do not pay for them, which results in an underprovision of those goods or services. For example, a free-rider may frequently ask for available parking lots (public goods) from those who have already paid for them, in order to benefit from free parking. That is, the free-rider may use the parking even more than the others without paying a penny. The free-rider problem is the question of how to limit free riding and its negative effects in these situations. The free-rider problem may occur when property rights are not clearly defined and imposed.
 
The free-rider problem is common with goods which are non-excludable, including public goods and situations of the Tragedy of the Commons.

Although the term "free rider" was first used in economic theory of public goods, similar concepts have been applied to other contexts, including collective bargaining, antitrust law, psychology and political science. For example, some individuals in a team or community may reduce their contributions or performance if they believe that one or more other members of the group may free ride.

The economic problem with free riding

Free riding is a problem of economic inefficiency when it leads to the under-production or over-consumption of a good. For example, when people are asked how much they value a particular public good, with that value measured in terms of how much money they would be willing to pay, their tendency is to under report their valuations.

Goods which are subject to free riding are usually characterized by the inability to exclude non-payers. This problem is sometimes compounded by the fact that common-property goods are characterized by rival consumption. Not only can consumers of common-property goods benefit without payment, but consumption by one imposes an opportunity cost on others. This will lead to overconsumption and even possibly exhaustion or destruction of the common-property good. If too many people start to free ride, a system or service will eventually not have enough resources to operate. 

The other problem of free-riding is experienced when the production of goods does not consider the external costs, particularly the use of ecosystem services.

Economic and political solutions

Assurance contracts

An assurance contract is a contract in which participants make a binding pledge to contribute to building a public good, contingent on a quorum of a predetermined size being reached. Otherwise the good is not provided and any monetary contributions are refunded.

A dominant assurance contract is a variation in which an entrepreneur creates the contract and refunds the initial pledge plus an additional sum of money if the quorum is not reached. (The entrepreneur profits by collecting a fee if the quorum is reached and the good is provided.) In game-theoretic terms this makes pledging to build the public good a dominant strategy: the best move is to pledge to the contract regardless of the actions of others. 

Coasian solution

A Coasian solution, named for the economist Ronald Coase, proposes that potential beneficiaries of a public good can negotiate to pool their resources and create it, based on each party's self-interested willingness to pay. His treatise, "The Problem of Social Cost" (1960), argued that if the transaction costs between potential beneficiaries of a public good are low—that it is easy for potential beneficiaries to find each other and organize a pooling their resources based upon the good's value to each of them—that public goods could be produced without government action.

Much later, Coase himself wrote that while what had become known as the Coase Theorem had explored the implications of zero transaction costs, he had actually intended to use this construct as a stepping-stone to understand the real world of positive transaction costs, corporations, legal systems and government actions:
I examined what would happen in a world in which transaction costs were assumed to be zero. My aim in doing so was not to describe what life would be like in such a world but to provide a simple setting in which to develop the analysis and, what was even more important, to make clear the fundamental role which transaction costs do, and should, play in the fashioning of the institutions which make up the economic system.
Coase also wrote:
The world of zero transaction costs has often been described as a Coasian world. Nothing could be further from the truth. It is the world of modern economic theory, one which I was hoping to persuade economists to leave. What I did in "The Problem of Social Cost" was simply to shed light on some of its properties. I argued in such a world the allocation of resources would be independent of the legal position, a result which Stigler dubbed the "Coase theorem".
Thus, while Coase himself appears to have considered the "Coase theorem" and Coasian solutions as simplified constructs to ultimately consider the real 20th-century world of governments and laws and corporations, these concepts have become attached to a world where transaction costs were much lower, and government intervention would unquestionably be less necessary. 

A minor alternative, especially for information goods, is for the producer to refuse to release a good to the public until payment to cover costs is met. Author Stephen King, for instance, authored chapters of a new novel downloadable for free on his website while stating that he would not release subsequent chapters unless a certain amount of money was raised. Sometimes dubbed holding for ransom, this method of public goods production is a modern application of the street performer protocol for public goods production. Unlike assurance contracts, its success relies largely on social norms to ensure (to some extent) that the threshold is reached and partial contributions are not wasted.

One of the purest Coasian solutions today is the new phenomenon of Internet crowdfunding. Here rules are enforced by computer algorithms and legal contracts as well as social pressure. For example, on the Kickstarter site, each funder authorizes a credit card purchase to buy a new product or receive other promised benefits, but no money changes hands until the funding goal is met. Because automation and the Internet so reduce the transaction costs for pooling resources, project goals of only a few hundred dollars are frequently crowdfunded, far below the costs of soliciting traditional investors.

Government provision

If voluntary provision of public goods will not work, then the solution is making their provision involuntary. This saves each of us from our own tendency to be a free rider, while also assuring us that no one else will be allowed to free ride. One frequently proposed solution to the problem is for governments or states to impose taxation to fund the production of public goods. This does not actually solve the theoretical problem because good government is itself a public good. Thus it is difficult to ensure the government has an incentive to provide the optimum amount even if it were possible for the government to determine precisely what amount would be optimum. These issues are studied by public choice theory and public finance.

Sometimes the government provides public goods using "unfunded mandates". An example is the requirement that every car be fit with a catalytic converter. This may be executed in the private sector, but the end result is predetermined by the state: the individually involuntary provision of the public good clean air. Unfunded mandates have also been imposed by the U.S. federal government on the state and local governments, as with the Americans with Disabilities Act, for example.

Regardless the role of the government is provide vital goods to all individuals, some of which they cannot obtain on themselves. In order to ensure that government services are properly funded taxes and other government controlled entities are enforced. Although enforced taxes deter the free-rider problem many contend that some goods should be excluded and made into private goods. However, this not possible with all goods such as pure public goods that are inseparable and inclusive, thus require "provision by public means". In short, the government has a responsibility to ensure that the social welfare of individuals is met as opposed to privatized goods.

Subsidies and joint products

A government may subsidize production of a public good in the private sector. Unlike government provision, subsidies may result in some form of a competitive market. The potential for cronyism (for example, an alliance between political insiders and the businesses receiving subsidies) can be limited with secret bidding for the subsidies or application of the subsidies following clear general principles. Depending on the nature of a public good and a related subsidy, principal–agent problems can arise between the citizens and the government or between the government and the subsidized producers; this effect and counter-measures taken to address it can diminish the benefits of the subsidy.

Subsidies can also be used in areas with a potential for non-individualism: For instance, a state may subsidize devices to reduce air pollution and appeal to citizens to cover the remaining costs. 

Similarly, a joint-product model analyzes the collaborative effect of joining a private good to a public good. For example, a tax deduction (private good) can be tied to a donation to a charity (public good). It can be shown that the provision of the public good increases when tied to the private good, as long as the private good is provided by a monopoly (otherwise the private good would be provided by competitors without the link to the public good).

Privileged group

The study of collective action shows that public goods are still produced when one individual benefits more from the public good than it costs him to produce it; examples include benefits from individual use, intrinsic motivation to produce, and business models based on selling complement goods. A group that contains such individuals is called a privileged group. A historical example could be a downtown entrepreneur who erects a street light in front of his shop to attract customers; even though there are positive external benefits to neighboring nonpaying businesses, the added customers to the paying shop provide enough revenue to cover the costs of the street light.

The existence of privileged groups may not be a complete solution to the free rider problem, however, as underproduction of the public good may still result. The street light builder, for instance, would not consider the added benefit to neighboring businesses when determining whether to erect his street light, making it possible that the street light isn't built when the cost of building is too high for the single entrepreneur even when the total benefit to all the businesses combined exceeds the cost. 

An example of the privileged group solution could be the Linux community, assuming that users derive more benefit from contributing than it costs them to do it. For more discussion on this topic see also Coase's Penguin

Another example is those musicians and writers who create music and writings for their own personal enjoyment, and publish because they enjoy having an audience. Financial incentives are not necessary to ensure the creation of these public goods. Whether this creates the correct production level of writings and music is an open question.

Merging free riders

Another method of overcoming the free rider problem is to simply eliminate the profit incentive for free riding by buying out all the potential free riders. A property developer that owned an entire city street, for instance, would not need to worry about free riders when erecting street lights since he owns every business that could benefit from the street light without paying. Implicitly, then, the property developer would erect street lights until the marginal social benefit met the marginal social cost. In this case, they are equivalent to the private marginal benefits and costs.

While the purchase of all potential free riders may solve the problem of underproduction due to free riders in smaller markets, it may simultaneously introduce the problem of underproduction due to monopoly. Additionally, some markets are simply too large to make a buyout of all beneficiaries feasible—this is particularly visible with public goods that affect everyone in a country.

Introducing an exclusion mechanism (club goods)

Another solution, which has evolved for information goods, is to introduce exclusion mechanisms which turn public goods into club goods. One well-known example is copyright and patent laws. These laws, which in the 20th century came to be called intellectual property laws, attempt to remove the natural non-excludability by prohibiting reproduction of the good. Although they can address the free rider problem, the downside of these laws is that they imply private monopoly power and thus are not Pareto-optimal

For example, in the United States, the patent rights given to pharmaceutical companies encourage them to charge high prices (above marginal cost) and to advertise to convince patients to persuade their doctors to prescribe the drugs. Likewise, copyright provides an incentive for a publisher to act like The Dog in the Manger, taking older works out of print so as not to cannibalize revenue from the publisher's own new works.

The laws also end up encouraging patent and copyright owners to sue even mild imitators in court and to lobby for the extension of the term of the exclusive rights in a form of rent seeking

These problems with the club-good mechanism arise because the underlying marginal cost of giving the good to more people is low or zero, but, because of the limits of price discrimination those who are unwilling or unable to pay a profit-maximizing price do not gain access to the good.

If the costs of the exclusion mechanism are not higher than the gain from the collaboration, club goods can emerge naturally. James M. Buchanan showed in his seminal paper that clubs can be an efficient alternative to government interventions.

On the other hand, the inefficiencies and inequities of club goods exclusions sometimes cause potentially excludable club goods to be treated as public goods, and their production financed by some other mechanism. Examples of such "natural" club goods include natural monopolies with very high fixed costs, private golf courses, cinemas, cable television and social clubs. This explains why many such goods are often provided or subsidized by governments, co-operatives or volunteer associations, rather than being left to be supplied by profit-minded entrepreneurs. These goods are often known as social goods.

Joseph Schumpeter claimed that the "excess profits", or profits over normal profit, generated by the copyright or patent monopoly will attract competitors that will make technological innovations and thereby end the monopoly. This is a continual process referred to as "Schumpeterian creative destruction", and its applicability to different types of public goods is a source of some controversy. The supporters of the theory point to the case of Microsoft, for example, which has been increasing its prices (or lowering its products' quality), predicting that these practices will make increased market shares for Linux and Apple largely inevitable.

A nation can be seen as a club whose members are its citizens. Government would then be the manager of this club. This is further studied in the Theory of the State.

Altruistic solutions

Social norms

When enough people do not think like free-riders, the private and voluntary provision of public goods may be successful. For example, a free rider might come to a public park to enjoy its beauty, yet discard litter that makes it less enjoyable for others. Other public-spirited individuals don't do this and might even pick up existing litter. Reasons for the act could be that the person derives pleasure from helping their community, feels ashamed if their neighbors or friends saw them, or could be emotionally attached to the public good. Even people who engaged in free-riding by littering elsewhere are less likely to if they see others hold on to their trash. 

Social norms can be observed wherever people interact, not only in physical spaces but in virtual communities on the Internet. For example, if a disabled person boards a crowded bus, everyone expects that some able-bodied person will volunteer their seat. The same social norm, although executed in a different environment, can also be applied to the Internet. If a user enters a discussion in a chat room and continues to use all capital letters or to make personal attacks ("flames") when addressing other users, the culprit may realize he or she has been blocked by other participants. As in real life, users learning to adapt to the social norms of cyberspace communities provide a public good—here, not suffering disruptive online behavior—for all the participants.

Social sanctions (punishment)

Experimental literature suggests that free riding can be overcome without any state intervention. Peer-to-peer punishment, that is, members sanction those members that do not contribute to the public good at a cost, is sufficient to establish and maintain cooperation. Such punishment is often considered altruistic, because it comes at a cost to the punisher, however, the exact nature remains to be explored. Whether costly punishment can explain cooperation is disputed. Recent research finds that costly punishment is less effective in real world environments. For example, punishment works relatively badly under imperfect information, where people cannot observe the behavior of others perfectly.

Voluntary organizations

Organizations such as the Red Cross, public radio, television, or a volunteer fire department provide public goods to the majority at the expense of a minority who voluntarily participate or contribute funds. Contributions to online collaborative media like Wikipedia and other wiki projects, and free software projects such as Linux are another example of relatively few contributors providing a public good (information) freely to all readers or software users. 

Proposed explanations for altruistic behavior include biological altruism and reciprocal altruism. For example, voluntary groups such as labor unions and charities often have a federated structure, probably in part because voluntary collaboration emerges more readily in smaller social groups than in large ones. 

While both biological and reciprocal altruism are observed in other animals, our species' complex social behaviors take these raw materials much farther. Philanthropy by wealthy individuals—some, such as Andrew Carnegie giving away their entire vast fortunes—have historically provided a multitude of public goods for others. One major impact was the Rockefeller Foundation's development of the "Green Revolution" hybrid grains that probably saved many millions of people from starvation in the 1970s. Christian missionaries, who typically spend large parts of their lives in remote, often dangerous places, have had disproportionate impact compared with their numbers worldwide for centuries. Communist revolutionaries in the 20th century had similar dedication and outsized impacts. International relief organizations such as Doctors Without Borders, Save the Children and Amnesty International have benefited millions, while also occasionally costing workers their lives. For better and for worse, humans can conceive of, and sacrifice for, an almost infinite variety of causes in addition to their biological kin.

Religions and ideologies

"The noblest motive is the public good." Thomas Jefferson Building, Library of Congress.
 
Voluntary altruistic organizations often motivate their members by encouraging deep-seated personal beliefs, whether religious or other (such as social justice or environmentalism) that are taken "on faith" more than proved by rational argument. When individuals resist temptations to free riding (e.g., stealing) because they hold these beliefs (or because they fear the disapproval of others who do), they provide others with public goods that might be difficult or impossible to "produce" by administrative coercion alone.

One proposed explanation for the ubiquity of religious belief in human societies is multi-level selection: altruists often lose out within groups, but groups with more altruists win. A group whose members believe a "practical reality" that motivates altruistic behavior may out-compete other groups whose members' perception of "factual reality" causes them to behave selfishly. A classic example is a soldier's willingness to fight for his tribe or country. Another example given in evolutionary biologist David Sloan Wilson's Darwin's Cathedral is the early Christian church under the late Roman Empire; because Roman society was highly individualistic, during frequent epidemics many of the sick died not of the diseases per se but for lack of basic nursing. Christians, who believed in an afterlife, were willing to nurse the sick despite the risks. Although the death rate among the nurses was high, the average Christian had a much better chance of surviving an epidemic than other Romans did, and the community prospered.

Religious and non-religious traditions and ideologies (such as nationalism and patriotism) are in full view when a society is in crisis and public goods such as defense are most needed. Wartime leaders invoke their God's protection and claim that their society's most hallowed traditions are at stake. For example, according to President Abraham Lincoln's Gettysburg Address during the American Civil War, the Union was fighting so "that government of the people, by the people, for the people, shall not perish from the earth". Such voluntary, if exaggerated, exhortations complement forcible measures—taxation and conscription—to motivate people to make sacrifices for their cause.

Collective action

From Wikipedia, the free encyclopedia
 
Collective action refers to action taken together by a group of people whose goal is to enhance their status and achieve a common objective. It is a term that has formulations and theories in many areas of the social sciences including psychology, sociology, anthropology, political science and economics.

The social identity model

Researchers Martijn van Zomeren, Tom Postmes, and Russell Spears conducted a meta-analysis of over 180 studies of collective action, in an attempt to integrate three dominant socio-psychological perspectives explaining antecedent conditions to this phenomenon – injustice, efficacy, and identity. In their resultant 2008 review article, an integrative Social Identity Model of Collective Action (SIMCA) was proposed which accounts for interrelationships among the three predictors as well as their predictive capacities for collective action. An important assumption of this approach is that people tend to respond to subjective states of disadvantage, which may or may not flow from objective physical and social reality.

Perceived injustice

Examining collective action through perceived injustice was initially guided by relative deprivation theory (RDT). RDT focuses on a subjective state of unjust disadvantage, proposing that engaging in fraternal (group-based) social comparisons with others may result in feelings of relative deprivation that foster collective action. Group-based emotions resulting from perceived injustice, such as anger, are thought to motivate collective action in an attempt to rectify the state of unfair deprivation. The extent to which individuals respond to this deprivation involves several different factors and varies from extremely high to extremely low across different settings. Meta-analysis results confirm that effects of injustice causally predict collective action, highlighting the theoretical importance of this variable.

Perceived efficacy

Moving beyond RDT, scholars suggested that in addition to a sense of injustice, people must also have the objective, structural resources necessary to mobilize change through social protest. An important psychological development saw this research instead directed towards subjective expectations and beliefs that unified effort (collective action) is a viable option for achieving group-based goals – this is referred to as perceived collective efficacy. Empirically, collective efficacy is shown to causally affect collective action among a number of populations across varied contexts.

Social identity

Social identity theory (SIT) suggests that people strive to achieve and maintain positive social identities associated with their group memberships. Where a group membership is disadvantaged (for example, low status), SIT implicates three variables in the evocation of collective action to improve conditions for the group – permeability of group boundaries, legitimacy of the intergroup structures, and the stability of these relationships. For example, when disadvantaged groups perceive intergroup status relationships as illegitimate and unstable, collective action is predicted to occur, in an attempt to change status structures for the betterment of the disadvantaged group.

Meta-analysis results also confirm that social identity causally predicts collective action across a number of diverse contexts. Additionally, the integrated SIMCA affords another important role to social identity – that of a psychological bridge forming the collective base from which both collective efficacy and group injustice may be conceived.

Model refinement

While there is sound empirical support for the causal importance of SIMCA’s key theoretical variables on collective action, more recent literature has addressed the issue of reverse causation, finding support for a related, yet distinct, encapsulation model of social identity in collective action (EMSICA). This model suggests that perceived group efficacy and perceived injustice provide the basis from which social identity emerges, highlighting an alternative causal pathway to collective action. Recent research has sought to integrate SIMCA with intergroup contact theory (see Cakal, Hewstone, Schwär, & Heath) and others have extended SIMCA through bridging morality research with the collective action literature (see van Zomeren, Postmes, & Spears for a review).

Public good

The economic theory of collective action is concerned with the provision of public goods (and other collective consumption) through the collaboration of two or more individuals, and the impact of externalities on group behavior. It is more commonly referred to as Public Choice. Mancur Olson's 1965 book The Logic of Collective Action: Public Goods and the Theory of Groups, is an important early analysis of the problems of public good cost. 

Besides economics, the theory has found many applications in political science, sociology, communication, anthropology and environmentalism.

Collective action problem

The term collective action problem describes the situation in which multiple individuals would all benefit from a certain action, but has an associated cost making it implausible that any individual can or will undertake and solve it alone. The ideal solution is then to undertake this as a collective action, the cost of which is shared. Situations like this include the prisoner's dilemma, a collective action problem in which no communication is allowed, the free rider problem, and the tragedy of the commons, also known as the problem with open access. An allegorical metaphor often used to describe the problem is "belling the cat".

Solutions to collective action problems include mutually binding agreements, government regulation, privatization, and assurance contracts, also known as crowd acting.

Exploitation of the great by the small

Mancur Olson made the claim that individual rational choice leads to situations where individuals with more resources will carry a higher burden in the provision of the public good than poorer ones. Poorer individuals will usually have little choice but to opt for the free rider strategy, i.e., they will attempt to benefit from the public good without contributing to its provision. This may also encourage the under-production (inefficient production) of the public good.

Institutional design

While public goods are often provided by governments, this is not always the case. Various institutional designs have been studied with the aim of reducing the collaborative failure. The best design for a given situation depends on the production costs, the utility function, and the collaborative effects, among other things. Here are only some examples:

Joint products

A joint-product model analyzes the collaborative effect of joining a private good to a public good. For example, a tax deduction (private good) can be tied to a donation to a charity (public good).

It can be shown that the provision of the public good increases when tied to the private good, as long as the private good is provided by a monopoly (otherwise the private good would be provided by competitors without the link to the public good).

Clubs

Some institutional design, e.g., intellectual property rights, can introduce an exclusion mechanism and turn a pure public good into an impure public good artificially.

If the costs of the exclusion mechanism are not higher than the gain from the collaboration, clubs can emerge. James M. Buchanan showed in his seminal paper that clubs can be an efficient alternative to government interventions.

A nation can be seen as a club whose members are its citizens. Government would then be the manager of this club.

Federated structure

In some cases, theory shows that collaboration emerges spontaneously in smaller groups rather than in large ones. This explains why labor unions or charities often have a federated structure.

In philosophy

Since the late 20th century, analytic philosophers have been exploring the nature of collective action in the sense of acting together, as when people paint a house together, go for a walk together, or together execute a pass play. These particular examples have been central for three of the philosophers who have made well known contributions to this literature: Michael Bratman, Margaret Gilbert, and John Searle, respectively. 

In (Gilbert 1989) and subsequent articles and book chapters including Gilbert (2006, chapter 7) Gilbert argues for an account of collective action according to which this rests on a special kind of interpersonal commitment, what Gilbert calls a "joint commitment". A joint commitment in Gilbert's sense is not a matter of a set of personal commitments independently created by each of the participants, as when each makes a personal decision to do something. Rather, it is a single commitment to whose creation each participant makes a contribution. Thus suppose that one person says "Shall we go for a walk?" and the other says "Yes, let's". Gilbert proposes that as a result of this exchange the parties are jointly committed to go for a walk, and thereby obligated to one another to act as if they were parts of a single person taking a walk. Joint commitments can be created less explicitly and through processes that are more extended in time. One merit of a joint commitment account of collective action, in Gilbert's view, is that it explains the fact that those who are out on a walk together, for instance, understand that each of them is in a position to demand corrective action of the other if he or she acts in ways that affect negatively the completion of their walk. In (Gilbert 2006a) she discusses the pertinence of joint commitment to collective actions in the sense of the theory of rational choice.

In Searle (1990) Searle argues that what lies at the heart of a collective action is the presence in the mind of each participant of a "we-intention". Searle does not give an account of we-intentions or, as he also puts it, "collective intentionality", but insists that they are distinct from the "I-intentions" that animate the actions of persons acting alone.

In Bratman (1993) Bratman proposed that, roughly, two people "share an intention" to paint a house together when each intends that the house is painted by virtue of the activity of each, and also intends that it is so painted by virtue of the intention of each that it is so painted. That these conditions obtain must also be "common knowledge" between the participants.

Discussion in this area continues to expand, and has influenced discussions in other disciplines including anthropology, developmental psychology, and economics. One general question is whether it is necessary to think in terms that go beyond the personal intentions of individual human beings properly to characterize what it is to act together. Bratman's account does not go beyond such personal intentions. Gilbert's account, with its invocation of joint commitment, does go beyond them. Searle's account does also, with its invocation of collective intentionality. The question of whether and how one must account for the existence of mutual obligations when there is a collective intention is another of the issues in this area of inquiry.

Spontaneous consensus

In addition to the psychological mechanisms of collective action as explained by the social identity model, researchers have developed sociological models of why collective action exists and have studied under what conditions collective action emerges. Along this social dimension, a special case of the general collective action problem is one of collective agreement: how does a group of agents (humans, animals, robots, etc.) reach consensus about a decision or belief in the absence of central organization? Common examples can be found from domains as diverse as biology (flocking, shoaling and schooling, and general collective animal behavior), economics (stock market bubbles), and sociology (social conventions and norms) among others.

Consensus is distinct from the collective action problem in that there often is not an explicit goal, benefit, or cost of action but rather it concerns itself with a social equilibrium of the individuals involved (and their beliefs). And it can be considered spontaneous when it emerges without the presence of a centralized institution among self-interested individuals.

Dimensions

Spontaneous consensus can be considered along 4 dimensions involving the social structure of the individuals participating (local versus global) in the consensus as well as the processes (competitive vs cooperative) involved in reaching consensus:
  • Competitive
  • Cooperative
  • Local
  • Global

Competitive versus cooperative

The underlying processes of spontaneous consensus can be viewed either as cooperation among individuals trying to coordinate themselves through their interactions or as competition between the alternatives or choices to be decided upon. Depending on the dynamics of the individuals involved as well as the context of the alternatives considered for consensus, the process can be wholly cooperative, wholly competitive, or a mix of the two.

Local versus global

The distinction between local and global consensus can be viewed in terms of the social structure underlying the network of individuals participating in the consensus making process. Local consensus occurs when there is agreement between groups of neighboring nodes while global consensus refers to the state in which most of the population has reached an agreement. How and why consensus is reached is dependent on both the structure of the social network of individuals as well as the presence (or lack) of centralized institutions.

Equilibrium mechanisms

There are many mechanisms (social and psychological) that have been identified to underlie the consensus making process. They have been used to both explain the emergence of spontaneous consensus and understand how to facilitate an equilibrium between individuals and can be grouped according to their role in the process.
  • Facilitation of Equilibrium
    • Communication
    • Punishment of Deviants
    • Positive Payoffs
    • Conformity Bias
  • Selection of Alternatives
    • Logical Reflection
    • Psychological and shared biases
    • Chance (when all alternatives are equivalent)

Methods and techniques

Due to the interdisciplinary nature of both the mechanisms as well as the applications of spontaneous consensus, a variety of techniques have been developed to study the emergence and evolution of spontaneous cooperation. Two of the most widely used are game theory and social network analysis.

Game theory

Traditionally game theory has been used to study zero-sum games but has been extended to many different types of games. Relevant to the study of spontaneous consensus are cooperative and non-cooperative games. Since a consensus must be reached without the presence of any external authoritative institution for it to be considered spontaneous, non-cooperative games and nash equilibrium have been the dominant paradigm for which to study its emergence.

In the context of non-cooperative games, a consensus is a formal nash equilibrium that all players tend towards through self-enforcing alliances or agreements.

Social network analysis

An alternative approach to studying the emergence of spontaneous consensus—that avoids many of the unnatural or overly constrained assumptions of game theoretic models—is the use of network based methods and social network analysis (SNA). These SNA models are theoretically grounded in the communication mechanism of facilitating consensus and describe its emergence through the information propagation processes of the network (behavioral contagion). Through the spread of influence (and ideas) between agents participating in the consensus, local and global consensus can emerge if the agents in the network achieve a shared equilibrium state. Leveraging this model of consensus, researchers have shown that local peer influence can be used to reach a global consensus and cooperation across the entire network. While this model of consensus and cooperation has been shown to be successful in certain contexts, research suggest that communication and social influence cannot be fully captured by simple contagion models and as such a pure contagion based model of consensus may have limits.

We need more powerful nuclear engines to explore farther and faster into space

Nuclear power has powered rockets for decades, but reaching deep space will require a big leap.

Last year, Voyager 2 finally broke through into interstellar space after traveling more than 11.2 billion miles. This epic mission was made possible by nuclear power, the technology that has powered spacecraft for decades.
Spacecraft like the Voyager pair are powered with radioisotope thermoelectric generators, or RTGs. These engines rely on the fact that radioactive substances release heat as they break down. By converting the heat generated by the decay of plutonium-238 (P-238) into electricity, spacecraft keep going long after the sun’s rays are a distant glimmer.

But RTGs are also constraining us. If we want to send spacecraft—or humans—farther, faster, and more often, we can’t keep relying on the same decades-old nuclear technologies. How can we expand our reach?
What’s happening right now

Our supply of plutonium-238 is running dry. The original batch was made in the US as a by-product of creating weapons-grade plutonium-239 during the Cold War. To keep exploring, NASA needs a lot more.

Oak Ridge National Lab took on the task of manufacturing it in 2012. It was a slow manual process to make even a few grams. But last month, researchers at Oak Ridge announced they’d finally developed a way to automate and scale up the production of neptunium and aluminum pellets needed to make P-238. The pellets are transformed into precious P-238 by pressing and enclosing them in aluminum tubing and irradiating them in a reactor. 
Creating these pellets was the biggest bottleneck in the process, and taking humans out of the equation took a lot of experimenting. “In a lot of nuclear work, it’s cook and look,” says program manager Bob Wham. “You design it, putting a lot of safety factors on design; take it out; and see if it performs like you expected.” After years of work automating the measuring and making, it did.

The lab now makes 50 grams of P-238 a year but expects to be up to 400 grams a year soon. It predicts it will be able to hit NASA’s annual target of 1.5 kg within two years. The more P-238 we have, the more missions we can send to deep space. 

Small steps

NASA has also investigated making more efficient RTGs called eMMRTGs, or enhanced multi-mission RTGs. But to really take a bigger step forward, we have to look at something new. “Eventually we will need higher-power systems. Only fission can supply that in any type of near-term scenario,” says Los Alamos National Laboratory researcher David Poston.
NASA
Poston is the chief reactor designer for Kilopower, a prototype fission reactor that NASA successfully testedlast year. It could provide power over the course of long missions, possibly even for human planetary outposts. “The way we evolved it to being feasible was simplifying things,” says Poston. “We’ve had plenty of space reactor programs over the past 30 years, but they’ve all failed. Mostly because they became too expensive.”  Kilopower currently has an output of 4 kilowatts, but researchers hope to reach 10 kW. 

Giant leaps

There have been some pie-in-the-sky nuclear ideas for a while, including detonating atom bombs out the back of spacecraft in what’s called nuclear pulse propulsion (you might be able to spot a few practical problems with that one). But some people are still working on making some equally crazy ideas a reality.

One of those teams is at Princeton Satellite Systems, which is looking to generate megawatts of power using fusion. Yes, we have gone from watts to kilowatts to megawatts. You’re probably familiar with fusion—it happens in the sky every day courtesy of our sun. Fusion produces several times the amount of energy fission creates, but it is hard to control. 

Princeton Satellite Systems is developing a direct fusion drive,which uses magnetic fields to generate current in plasma and heat it up to 1 billion °C. The team says the thrust the minivan-size machine would (theoretically) produce would cut inter-solar-system travel times by more than half (trips to Pluto would take about four years rather than nine), with power to spare.
Oak Ridge National Laboratory, U.S. Dept. of Energy
“If you have power when you get there, you can do a lot of really cool experiments,” says the firm’s physicist Charles Swanson. “One of the coolest things Cassini did is radar images of Saturn’s moon Titan. But radar is power hungry and was limited. Having a megawatt of power frees up options.”

The company has received a boatload of funding from NASA and the US Department of Energy, so it looks as if someone believes this moonshot could work. But let’s be frank: it isn’t going to happen anytime soon—or even in our lifetime. Fusion is still in the earliest stages of research here on Earth.

Even so, it’s still fun to imagine what it might make possible. It could be the leap we need to fast-track our trips to the outer planets and beyond.

Inequality (mathematics)

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Inequality...