Volunteer's dilemma

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The volunteer's dilemma game models a situation in which each player can either make a small sacrifice that benefits everybody, or instead wait in hope of benefiting from someone else's sacrifice.

Game theory is the study of mathematical models of strategic interaction among rational decision-makers. It has applications in all fields of social science, as well as in logic, systems science, and computer science. Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of 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.

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One example is a scenario in which the electricity supply has failed for an entire neighborhood. All inhabitants know that the electricity company will fix the problem as long as at least one person calls to notify them, at some cost. If no one volunteers, the worst possible outcome is obtained for all participants. If any one person elects to volunteer, the rest benefit by not doing so. [1]

A public good is only produced if at least one person volunteers to pay an arbitrary cost. In this game, bystanders decide independently on whether to sacrifice themselves for the benefit of the group. Because the volunteer receives no benefit, there is a greater incentive for freeriding than to sacrifice oneself for the group. If no one volunteers, everyone loses. The social phenomena of the bystander effect and diffusion of responsibility heavily relate to the volunteer's dilemma.[ citation needed ]

Public good (economics) Good that is non-excludable and non-rival

In economics, a public good is a good that is both non-excludable and non-rivalrous in that individuals cannot be excluded from use or could be enjoyed without paying for it, and where use by one individual does not reduce availability to others or the goods can be effectively consumed simultaneously by more than one person. This is in contrast to a common good such as wild fish stocks in the ocean, which is non-excludable but is rivalrous to a certain degree, as if too many fish are harvested, the stocks will be depleted.

The bystander effect, or bystander apathy, is a social psychological claim that individuals are less likely to offer help to a victim when other people are present; the greater the number of bystanders, the less likely it is that one of them will help.

Diffusion of responsibility is a sociopsychological phenomenon whereby a person is less likely to take responsibility for action or inaction when others are present. Considered a form of attribution, the individual assumes that others either are responsible for taking action or have already done so.

Payoff matrix

The payoff matrix for the game is shown below:

Volunteer's dilemma payoff matrix (example)
at least one other person cooperatesall others defect
cooperate00
defect1−10

When the volunteer's dilemma takes place between only two players, the game gets the character of the game 'chicken'. As seen by the payoff matrix, there is no dominant strategy in the volunteer's dilemma. In a mixed-strategy Nash equilibrium, an increase in N players will decrease the likelihood that at least one person volunteers, which is a result of the bystander effect.

The game of chicken, also known as the hawk–dove game or snowdrift game, is a model of conflict for two players in game theory. The principle of the game is that while it is to both players’ benefit if one player yields, the other player's optimal choice depends on what their opponent is doing: if the player opponent yields, they should not, but if the opponent fails to yield, the player should.

In game theory, the Nash equilibrium, named after the mathematician John Forbes Nash Jr., is a proposed solution of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.

Examples in real life

The murder of Kitty Genovese

The story of Kitty Genovese is often cited as an example of the volunteer's dilemma. Genovese was stabbed to death outside her apartment building in Queens, New York, in 1964. According to a highly influential New York Times account, dozens of people witnessed the assault but did not get involved because they thought others would contact the police anyway and did not want to incur the personal cost of getting involved. [2] Subsequent investigations have shown the original account to have been unfounded, and although it inspired sound scientific research, its use as a simplistic parable in psychology textbooks has been criticized. [3]

The meerkat

The meerkat exhibits the volunteer's dilemma in nature. One or more meerkats act as sentries while the others forage for food. If a predator approaches, the sentry meerkat lets out a warning call so the others can burrow to safety. However, the altruism of this meerkat puts it at risk of being discovered by the predator.

Meerkat species of small carnivoran in the mongoose family (Herpestidae)

The meerkat or suricate is a small carnivoran in the mongoose family. It is the only member of the genus Suricata. Meerkats live in all parts of the Kalahari Desert in Botswana, in much of the Namib Desert in Namibia and southwestern Angola, and in South Africa. A group of meerkats is called a "mob", "gang" or "clan". A meerkat clan often contains about 20 meerkats, but some super-families have 50 or more members. In captivity, meerkats have an average life span of 12–14 years, and about 6–7 years in the wild.

See also

Related Research Articles

Altruism Principle or practice of concern for the welfare of others

Altruism is the principle and moral practice of concern for happiness of other human beings and/or animals, resulting in a quality of life both material and spiritual. It is a traditional virtue in many cultures and a core aspect of various religious traditions and secular worldviews, though the concept of "others" toward whom concern should be directed can vary among cultures and religions. In an extreme case, altruism may become a synonym of selflessness which is the opposite of selfishness.

In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. Thus, cutting a cake, where taking a larger piece reduces the amount of cake available for others, is a zero-sum game if all participants value each unit of cake equally.

The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it "prisoner's dilemma", presenting it as follows:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:

In economics and game theory, a participant is considered to have superrationality if they have perfect rationality but assume that all other players are superrational too and that a superrational individual will always come up with the same strategy as any other superrational thinker when facing the same problem. Applying this definition, a superrational player playing against a superrational opponent in a prisoner's dilemma will cooperate while a rationally self-interested player would defect.

In the early hours of March 13, 1964, 28-year-old Kitty Genovese was stabbed outside the apartment building across the street from where she lived in an apartment above a row of shops on Austin street in Kew Gardens, Queens, a borough of New York City. Two weeks after the murder, The New York Times published an article claiming that 38 witnesses saw or heard the attack, but none of them called the police or came to her aid.

Abraham Michael "Abe" Rosenthal was an American journalist who served as The New York Times executive editor from 1977 to 1988, having served previously as the city editor and managing editor. At the end of his tenure as executive editor, he became a columnist (1987–1999) and New York Daily News columnist (1999–2004).

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In game theory, coordination games are a class of games with multiple pure strategy Nash equilibria in which players choose the same or corresponding strategies.

A social dilemma is a situation in which an individual profits from selfishness unless everyone chooses the selfish alternative, in which case the whole group loses. Problems arise when too many group members choose to pursue individual profit and immediate satisfaction rather than behave in the group's best long-term interests. Social dilemmas can take many forms and are studied across disciplines such as psychology, economics, and political science. Examples of phenomena that can be explained using social dilemmas include resource depletion, low voter turnout, and overpopulation.

In game theory, the stag hunt is a game that describes a conflict between safety and social cooperation. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Jean-Jacques Rousseau described a situation in which two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each player must choose an action without knowing the choice of the other. If an individual hunts a stag, they must have the cooperation of their partner in order to succeed. An individual can get a hare by himself, but a hare is worth less than a stag. This has been taken to be a useful analogy for social cooperation, such as international agreements on climate change.

Public goods game

The public goods game is a standard of experimental economics. In the basic game, subjects secretly choose how many of their private tokens to put into a public pot. The tokens in this pot are multiplied by a factor and this "public good" payoff is evenly divided among players. Each subject also keeps the tokens they do not contribute.

In game theory, 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 one can change the identities of the players without changing the payoff to the strategies, then a game is symmetric. Symmetry can come in different varieties. Ordinally symmetric games are games that are symmetric with respect to the ordinal structure of the payoffs. A game is quantitatively symmetric if and only if it is symmetric with respect to the exact payoffs. A partnership game is a symmetric game where both players receive identical payoffs for any strategy set. That is, the payoff for playing strategy a against strategy b receives the same payoff as playing strategy b against strategy a.

In game theory, the traveler's dilemma is a non-zero-sum game in which each player proposes a payoff. The lower of the two proposals wins; the lowball player receives the lowball payoff plus a small bonus, and the highball player receives the same lowball payoff, minus a small penalty. Surprisingly, the Nash equilibrium is for both players to aggressively lowball. The traveler's dilemma is notable in that naive play appears to outperform the Nash equilibrium; this apparent paradox also appears in the centipede game and the finitely-iterated prisoner's dilemma.

Rabin fairness is a fairness model invented by Matthew Rabin. It goes beyond the standard assumptions in modeling behavior, rationality and self-interest, to incorporate fairness. Rabin's fairness model incorporates findings from the fields of economics and psychology fields to provide an alternative utility model. Fairness is one type of social preference.

In Psychology and Sociology, a Social Experiment is a category of Human Research which test a human’s reaction to certain situations or event. This is typically done by having two different groups of people and have one participate in an event/program and the other react to the event/program. Over a period of hours, days, months or years, the two differing groups are monitored to see the effects and differences as a result of the experiment.

Vigilance, in the field of behavioural ecology, refers to an animal's examination of its surroundings in order to heighten awareness of predator presence. Vigilance is an important behaviour during foraging as animals must often venture away from the safety of shelter to find food. However being vigilant comes at the expense of time spent feeding so there is a trade-off between the two. The length of time animals devote to vigilance is dependent on many factors including predation risk and hunger.

The Optional Prisoner's Dilemma (OPD) game models a situation of conflict involving two players in game theory. It can be seen as an extension of the standard prisoner's dilemma game, where players have the option to "reject the deal", that is, to abstain from playing the game. This type of game can be used as a model for a number of real world situations in which agents are afforded the third option of abstaining from a game interaction such as an election.

Reciprocal altruism in humans refers to an individual behavior that gives benefit conditionally upon receiving a returned benefit, which draws on the economic concept – ″gains in trade″. Human reciprocal altruism would include the following behaviors : helping patients, the wounded, and the others when they are in crisis; sharing food, implement, knowledge.

References

  1. Poundstone, William (1993). Prisoner's Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb. New York: Anchor Books. ISBN   978-0-385-41580-4.
  2. Weesie, Jeroen (1993). "Asymmetry and Timing in the Volunteer's Dilemma". Journal of Conflict Resolution . 37 (3): 569–590. doi:10.1177/0022002793037003008. JSTOR   174269.
  3. Manning, R.; Levine, M; Collins, A. (September 2007). "The Kitty Genovese murder and the social psychology of helping: The parable of the 38 witnesses". American Psychologist . 62 (6): 555–562. CiteSeerX   10.1.1.210.6010 . doi:10.1037/0003-066X.62.6.555. PMID   17874896.