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Encyclopedia > Prisoner's dilemma
Will the two prisoners cooperate, or will both of them betray to lessen their own terms, ending up with longer ones?

The Prisoner's Dilemma constitutes a problem in game theory. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "Prisoner's Dilemma" name (Poundstone, 1992). Game theory is a branch of applied mathematics that is often used in the context of economics. ... Image File history File links Prison. ... Game theory is a branch of applied mathematics that is often used in the context of economics. ... Merrill Meeks Flood was a mathematician, notable for developing, with Melvin Dresher, the the game theoretical Prisoners dilemma model of cooperation and conflict while at RAND in 1950. ... Melvin Dresher was a mathematician, notable for developing, with Merrill Flood, the game theoretical model of cooperation and conflict known as the Prisoners dilemma while at RAND in 1950. ... The RAND Corporation is a nonprofit global policy think tank first formed to offer research and analysis to the United States armed forces. ... Albert W. Tucker was chairman of the mathematics department at Princeton. ...

In its "classical" form, the prisoner's dilemma (PD) is presented as follows:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies ("defects") for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

The prisoner's dilemma forms a non-zero-sum game in which two players may each "cooperate" with or "defect" from (i.e., betray) the other player. In this game, as in all game theory, the only concern of each individual player ("prisoner") is maximizing his/her own payoff, without any concern for the other player's payoff. The unique equilibrium for this game is a Pareto-suboptimal solution—that is, rational choice leads the two players to both play defect even though each player's individual reward would be greater if they both played cooperate. Zero-sum describes a situation in which a participants gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). ... Pareto efficiency, or Pareto optimality, is an important notion in neoclassical economics with broad applications in game theory, engineering and the social sciences. ...

In the classic form of this game, cooperating is strictly dominated by defecting, so that the only possible equilibrium for the game is for all players to defect. In simpler terms, no matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect, all things being equal. In game theory, dominance occurs when one strategy is better or worse than another regardless of the strategies of a players opponents. ... In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ... In economics and game theory, the participants are sometimes considered to have perfect rationality: that is, they always act in a rational way, and are capable of arbitrarily complex deductions towards that end. ...

In the iterated prisoner's dilemma the game is played repeatedly. Thus each player has an opportunity to "punish" the other player for previous non-cooperative play. Cooperation may then arise as an equilibrium outcome. The incentive to defect is overcome by the threat of punishment, leading to the possibility of a cooperative outcome. So if the game is infinitely repeated, cooperation may be a subgame perfect Nash equilibrium although both players defecting always remains an equilibrium and there are many other equilibrium outcomes. In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). ... Subgame perfect equilibrium is an economics term used in game theory to describe an equilibrium such that players strategies constitute a Nash equilibrium in every subgame of the original game. ...

Strategy for the classical prisoner's dilemma

The classical prisoner's dilemma can be summarized thus:

Prisoner B Stays Silent Prisoner B Betrays
Prisoner A Stays Silent Each serves 6 months Prisoner A: 10 years
Prisoner B: goes free
Prisoner A Betrays Prisoner A: goes free
Prisoner B: 10 years
Each serves 5 years

In this game, regardless of what the opponent chooses, each player always receives a higher payoff (lesser sentence) by betraying; that is to say that betraying is the strictly dominant strategy. However, if the other player acts similarly, then they both betray and both get a lower payoff than they would get by staying silent. Rational self-interested decisions result in each prisoner's being worse off than if each chose to lessen the sentence of the accomplice at the cost of staying a little longer in jail himself. Hence a seeming dilemma. In game theory, this demonstrates very elegantly that in a non-zero sum game a Nash Equilibrium need not be a Pareto optimum. In game theory, dominance occurs when one strategy is better or worse than another regardless of the strategies of a players opponents. ... Game theory is a branch of applied mathematics that is often used in the context of economics. ... Zero-sum describes a situation in which a participants gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). ... In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ... Pareto efficiency, or Pareto optimality, is a central concept in game theory with broad applications in economics, engineering and the social sciences. ...

Generalized form

We can expose the skeleton of the game by stripping it of the prisoner framing device. The generalized form of the game has been used frequently in experimental economics. The following rules give a typical realization of the game. The term framing device refers to the usage of the same single action, scene, event, setting, or any element of significance at both the beginning and end of an artistic, musical, or literary work. ... Experimental economics is the use of experimental methods to evaluate theoretical predictions of economic behaviour. ...

There are two players and a banker. Each player holds a set of two cards: one printed with the word "Cooperate", the other printed with "Defect" (the standard terminology for the game). Each player puts one card face-down in front of the banker. By laying them face down, the possibility of a player knowing the other player's selection in advance is eliminated (although revealing one's move does not affect the dominance analysis[1]). At the end of the turn, the banker turns over both cards and gives out the payments accordingly.

If player 1 (red) defects and player 2 (blue) cooperates, player 1 gets the Temptation to Defect payoff of 5 points while player 2 receives the Sucker's payoff of 0 points. If both cooperate they get the Reward for Mutual Cooperation payoff of 3 points each, while if they both defect they get the Punishment for Mutual Defection payoff of 1 point. The checker board payoff matrix showing the payoffs is given below. It has been suggested that this article or section be merged with normal form game. ...

Cooperate Defect 3, 3 0, 5 5, 0 1, 1

In "win-lose" terminology the table looks like this:

Cooperate Defect win-win lose much-win much win much-lose much lose-lose

These point assignments are given arbitrarily for illustration. It is possible to generalize them, as follows:

Cooperate Defect R, R S, T T, S P, P

Where T stands for Temptation to defect, R for Reward for mutual cooperation, P for Punishment for mutual defection and S for Sucker's payoff. The following inequalities must hold:

T > R > P > S

In addition to the above condition, if the game is repeatedly played by two players, the following condition should be added.[2]

2 R > T + S

If that condition does not hold, then full cooperation is not necessarily Pareto optimal, as the players are collectively better off by having each player alternate between cooperate and defect. Pareto efficiency, or Pareto optimality, is a central concept in economics with broad applications in game theory, engineering and the social sciences. ...

These rules were established by cognitive scientist Douglas Hofstadter and form the formal canonical description of a typical game of Prisoner's Dilemma. Douglas Richard Hofstadter (born February 15, 1945 in New York, New York) is an American academic. ...

A simple special case occurs when the advantage of defection over cooperation is independent of what the co-player does and cost of the co-players defection is independent of one's own action, i.e. T+S = P+R.

Human behavior in the Prisoner's Dilemma

One experiment based on the simple dilemma found that approximately 40% of participants played "cooperate" (i.e., stayed silent).[3] Experimental economics is the use of experimental methods to evaluate theoretical predictions of economic behaviour. ...

The iterated prisoner's dilemma

If two players play Prisoner's Dilemma more than once in succession (that is, having memory of at least one previous game), it is called iterated Prisoner's Dilemma. Amongst results shown by Nobel Prize winner Robert Aumann in his 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome. Popular interest in the iterated prisoners dilemma (IPD) was kindled by Robert Axelrod in his book The Evolution of Cooperation (1984). In this he reports on a tournament he organized in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth. Israel Robert John Aumann (×™×©×¨××œ ××•×ž×Ÿ) (born June 8, 1930) is an Israeli mathematician and a member of the United States National Academy of Sciences. ... Robert Axelrod is the Arthur W. Bromage Distinguished University Professor of Political Science and Public Policy at the University of Michigan. ... The Evolution of Cooperation is a 1984 book and a 1981 article of the same title by political science professor Robert Axelrod. ...

Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more altruistic strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by natural selection. For the ethical doctrine, see Altruism (ethics). ... For other uses, see Natural selection (disambiguation). ...

The best deterministic strategy was found to be "Tit for Tat," which Anatol Rapoport developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of BASIC, and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his opponent did on the previous move. Depending on the situation, a slightly better strategy can be "Tit for Tat with forgiveness." When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1%-5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents. In computer science, a deterministic algorithm is an algorithm which, in informal terms, behaves predictably. ... Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ... Anatol Rapoport (born May 22, 1911) is a Russian-born American Jewish, mathematical psychologist. ...

By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.

Nice
The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes refered to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore a purely selfish strategy will not "cheat" on its opponent, for purely utilitarian reasons first.
Retaliating
However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such softies.
Forgiving
Another quality of successful strategies is that they must be forgiving. Though they will retaliate, they will once again fall back to cooperating if the opponent does not continue to play defects. This stops long runs of revenge and counter-revenge, maximizing points.
Non-envious
The last quality is being non-envious, that is not striving to score more than the opponent (impossible for a ‘nice’ strategy, i.e., a 'nice' strategy can never score more than the opponent).

Therefore, Axelrod reached the Utopian-sounding conclusion that selfish individuals for their own selfish good will tend to be nice and forgiving and non-envious. For other uses, see Utopia (disambiguation). ...

The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the Tit-for-Tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being Tit-for-Tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.

A strategy called Pavlov (an example of Win-Stay, Lose-Switch) cooperates at the first iteration and whenever the player and co-player did the same thing at the previous iteration; Pavlov defects when the player and co-player did different things at the previous iteration. For a certain range of parameters, Pavlov beats all other strategies by giving preferential treatment to co-players which resemble Pavlov.

Deriving the optimal strategy is generally done in two ways:

1. Bayesian Nash Equilibrium: If the statistical distribution of opposing strategies can be determined (e.g. 50% tit-for-tat, 50% always cooperate) an optimal counter-strategy can be derived analytically.[4]
2. Monte Carlo simulations of populations have been made, where individuals with low scores die off, and those with high scores reproduce (a genetic algorithm for finding an optimal strategy). The mix of algorithms in the final population generally depends on the mix in the initial population. The introduction of mutation (random variation during reproduction) lessens the dependency on the initial population; empirical experiments with such systems tend to produce Tit-for-Tat players (see for instance Chess 1988), but there is no analytic proof that this will always occur.

Although Tit-for-Tat is considered to be the most robust basic strategy, a team from Southampton University in England (led by Professor Nicholas Jennings [1] and consisting of Rajdeep Dash, Sarvapali Ramchurn, Alex Rogers, Perukrishnen Vytelingum) introduced a new strategy at the 20th-anniversary Iterated Prisoner's Dilemma competition, which proved to be more successful than Tit-for-Tat. This strategy relied on cooperation between programs to achieve the highest number of points for a single program. The University submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start. Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result,[5] this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom. In game theory, a Bayesian game is one in which information about characteristics of the other players (i. ... The Monte Carlo method can be illustrated as a game of battleship. ... A genetic algorithm (GA) is a search technique used in computing to find exact or approximate solutions to optimization and search problems. ... The University of Southampton is a British university, with a reputation for quality research. ...

This strategy takes advantage of the fact that multiple entries were allowed in this particular competition, and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of minmaxing). In a competition where one has control of only a single player, Tit-for-Tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analysing single agent strategies as compared to Axelrod's seminal tournament. However, it provided the framework for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Richard Dawkins in his book The Selfish Gene pointed out the possibility of such strategies winning if multiple entries were allowed, but remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players. When the Southampton programs engage in an opening "ten move dance" to recognize one another, this only reinforces just how valuable communication can be in shifting the balance of the game. Min-maxing is the practice of playing a role-playing game for the intent of creating the best character by means of minimizing undesired traits and maximizing desired ones. ... The Selfish Gene is a book on evolution by Richard Dawkins, published in 1976. ...

If an iterated PD is going to be iterated exactly N times, for some known constant N, then it is always optimal to defect in all rounds. The only possible Nash equilibrium is to always defect. The proof goes like this: one might as well defect on the last turn, since the opponent will not have a chance to punish the player. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. For cooperation to emerge the total number of rounds must be random, or at least unknown to the players. However, even in this case always defect is no longer a strictly dominant strategy, only a Nash equilibrium. Another odd case is "play forever" prisoner's dilemma. The game is repeated infinitely many times, and the player's score is the average (suitably computed). In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ...

The prisoner's dilemma game is fundamental to certain theories of human cooperation and trust. On the assumption that the PD can model transactions between two people requiring trust, cooperative behaviour in populations may be modelled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "Peace-War game".[6] Genghis Khans empire over time An iterated game originally played in academic groups and by computer simulation for years to study possible strategies of cooperation and aggression. ...

Learning psychology and game theory

Where game players can learn to estimate the likelihood of other players defecting, their own behaviour is influenced by their experience of the others' behaviour. Simple statistics show that inexperienced players are more likely to have had, overall, atypically good or bad interactions with other players. If they act on the basis of these experiences (by defecting or cooperating more than they would otherwise) they are likely to suffer in future transactions. As more experience is accrued a truer impression of the likelihood of defection is gained and game playing becomes more successful. The early transactions experienced by immature players are likely to have a greater effect on their future playing than would such transactions affect mature players. This principle goes part way towards explaining why the formative experiences of young people are so influential and why, for example, those who are particularly vulnerable to bullying sometimes become bullies themselves.

The likelihood of defection in a population may be reduced by the experience of cooperation in earlier games allowing trust to build up.[7] Hence self-sacrificing behaviour may, in some instances, strengthen the moral fibre of a group. If the group is small the positive behaviour is more likely to feed back in a mutually affirming way, encouraging individuals within that group to continue to cooperate. This is allied to the twin dilemma of encouraging those people whom one would aid to indulge in behaviour that might put them at risk. Such processes are major concerns within the study of reciprocal altruism, group selection, kin selection and moral philosophy. Trust is the belief in the good character of one party, presumed to seek to fulfill policies, ethical codes, law and their previous promises. ... In evolutionary biology, reciprocal altruism is a form of altruism in which one organism provides a benefit to another in the expectation of future reciprocation. ... In evolutionary biology, group selection refers to the idea that alleles can become fixed or spread in a population because of the benefits they bestow on groups, regardless of the fitness of individuals within that group. ... In evolutionary biology, kin selection refers to changes in gene frequency across generations that are driven at least in part by interactions between related individuals, and this forms much of the conceptual basis of the theory of social evolution. ... Ethics is the branch of axiology â€“ one of the four major branches of philosophy, alongside metaphysics, epistemology, and logic â€“ which attempts to understand the nature of morality; to define that which is right from that which is wrong. ...

Rationality and super-rationality according to Douglas Hofstadter

Douglas Hofstadter in his Metamagical Themas proposed to reject the definition of "rational" that led "rational" players to defect. In his view, truly rational (or "superrational") players take into account that the other person is (presumably) superrational, like them, and thus they behave identically, and thus they cooperate. This view of the one-shot PD is in complete contradiction with its definition, as it assumes the symmetry between the two players: Douglas Richard Hofstadter (born February 15, 1945 in New York, New York) is an American academic. ... Douglas Richard Hofstadter (born February 15, 1945 in New York, New York) is an American academic. ... Metamagical Themas is an eclectic collection of articles written for Scientific American during the early 1980s by Douglas Hofstadter, and published together as a book in 1985 by Basic Books (ISBN 0465045669) . The subject matter of the articles is loosely woven about themes in philosophy, creativity, artificial intelligence and important... The concept of superrationality is discussed in Douglas Hofstadters book Metamagical Themas. Superrationality is based on the idea that two perfect logicians will come up with the same, correct, answer to a logical or mathematical problem. ...

• an optimal strategy must be the same for both players (unlike the terms of the classical PD)
• the result must lie on the diagonal of the payoff matrix
• maximize return from solutions on the diagonal, hence cooperate

Morality

While it is sometimes thought that morality must involve the constraint of self-interest, David Gauthier famously argues that co-operating in the prisoners dilemma on moral principles is consistent with self-interest and the axioms of game theory.[citation needed] In his opinion, it is most prudent to give up straightforward maximizing and instead adopt a disposition of constrained maximization, according to which one resolves to cooperate in the belief that the opponent will respond with the same choice, while in the classical PD it is explicitly stipulated that the response of the opponent does not depend on the player's choice. This form of contractarianism claims that good moral thinking is just an elevated and subtly strategic version of plain old means-end reasoning. Morality (from the Latin manner, character, proper behavior) has three principal meanings. ... David Gauthier (born 1932) is a Canadian-American philosopher best known for his neo-Hobbesian social contract (contractarian) theory of morality, as laid out in his book Morals By Agreement. ... Social contract is a phrase used in philosophy, political science, and sociology to denote a real or hypothetical agreement within a state regarding the rights and responsibilities of the state and its citizens, or more generally a similar concord between a group and its members. ...

Douglas Hofstadter expresses a strong personal belief that the mathematical symmetry is reinforced by a moral symmetry, along the lines of the Kantian categorical imperative: defecting in the hope that the other player cooperates is morally indefensible.[citation needed] If players treat each other as they would treat themselves, then they will cooperate. Douglas Richard Hofstadter (born February 15, 1945 in New York, New York) is an American academic. ... Immanuel Kant Immanuel Kant (April 22, 1724 – February 12, 1804) was a Prussian philosopher, generally regarded as one of Europes most influential thinkers and the last major philosopher of the Enlightenment. ... The categorical imperative is the central philosophical concept of the moral philosophy of Immanuel Kant, and of modern deontological ethics. ...

Real-life examples

These particular examples, involving prisoners and bag switching and so forth, may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics and sociology, as well as to the biological sciences such as ethology and evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of Prisoner's Dilemma (PD). This wide applicability of the PD gives the game its substantial importance. The social sciences are groups of academic disciplines that study the human aspects of the world. ... Face-to-face trading interactions on the New York Stock Exchange trading floor. ... For other uses, see Politics (disambiguation). ... Sociology (from Latin: socius, companion; and the suffix -ology, the study of, from Greek Î»ÏŒÎ³Î¿Ï‚, lÃ³gos, knowledge [1]) is the scientific or systematic study of society, including patterns of social relationships, social interaction, and culture[2]. Areas studied in sociology can range from the analysis of brief contacts between anonymous... This article does not cite any references or sources. ... This article or section does not cite any references or sources. ...

In political science, for instance, the PD scenario is often used to illustrate the problem of two states engaged in an arms race. Both will reason that they have two options, either to increase military expenditure or to make an agreement to reduce weapons. Neither state can be certain that the other one will keep to such an agreement; therefore, they both incline towards military expansion. The paradox is that both states are acting rationally, but producing an apparently irrational result. This could be considered a corollary to deterrence theory. The Politics series Politics Portal This box:      Political Science is the field concerning the theory and practice of politics and the description and analysis of political systems and political behaviour. ... The term arms race in its original usage describes a competition between two or more parties for military supremacy. ... Source: SIPRI Military Expenditure Project Website Military expenditure is an indicator of the economic resources devoted to military purposes. ... Look up paradox in Wiktionary, the free dictionary. ... Rationality as a term is related to the idea of reason, a word which following Websters may be derived as much from older terms referring to thinking itself as from giving an account or an explanation. ... A theorem is a statement which can be proven true within some logical framework. ... Deterrence theory is a defensive strategy developed after World War II and used throughout the Cold War. ...

In sociology or criminology, the PD may be applied to an actual dilemma facing two inmates. The game theorist Marek Kaminski, a former political prisoner, analysed the factors contributing to payoffs in the game set up by a prosecutor for arrested defendants (cf. References). He concluded that while the PD is the ideal game of a prosecutor, numerous factors may strongly affect the payoffs and potentially change the properties of the game. Sociology (from Latin: socius, companion; and the suffix -ology, the study of, from Greek Î»ÏŒÎ³Î¿Ï‚, lÃ³gos, knowledge [1]) is the scientific or systematic study of society, including patterns of social relationships, social interaction, and culture[2]. Areas studied in sociology can range from the analysis of brief contacts between anonymous... Criminology is the scientific study of crime as an individual and social phenomenon. ...

In program management and technology development, the PD applies to the relationship between the customer and the developer. Capt Dan Ward, an officer in the US Air Force, examined The Program Manager's Dilemma in an article published in Defense AT&L, a defense technology journal.[8]

Another example concerns a well-known concept in cycling races, for instance in the Tour de France. Consider two cyclists halfway in a race, with the peloton (larger group) at great distance behind them. The two cyclists often work together (mutual cooperation) by sharing the tough load of the front position, where there is no shelter from the wind. If neither of the cyclists makes an effort to stay ahead, the peloton will soon catch up (mutual defection). An often-seen scenario is one cyclist doing the hard work alone (cooperating), keeping the two ahead of the peloton. In the end, this will likely lead to a victory for the second cyclist (defecting) who has an easy ride in the first cyclist's slipstream. Police officer on a bicycle Cycling is a means of transport, a form of recreation and a sport. ... For other uses, see Tour de France (disambiguation). ... The peloton (from French, literally meaning ball and related to the English word platoon), bunch or pack is the large main group in a road bicycle race. ... dddeath ...

Also in athletics, there is a widespread practice in high school wrestling where the participants intentionally lose unnaturally large amounts of weight so as to compete against lighter opponents. In doing so, the participants are clearly not at their top level of physical and athletic fitness and yet often end up competing against the same opponents anyway, who have also followed this practice (mutual defection). The result is a reduction in the level of competition. Yet if a participant maintains their natural weight (cooperating), they will most likely compete against a stronger opponent who has lost considerable weight.

Large software projects under the GPL (such as Linux) can force cooperation in an otherwise standard PD situation. Given a piece of Free Software, you can study the (modifiable) source code and make improvements. Then you can keep secret the improved version, i.e. keep the modified source code to yourself and distribute it in an unmodifiable binary form (defect). Alternatively, you could share the improved version in a modifiable source code form (cooperate). If everyone defects, then many are probably making exactly the same improvements. For any software that is under the GPL, it is illegal to distribute only the unmodifiable form, including any changes made, thus forcing cooperation. Hence, rival parties can all work on it and know that none will defect, and all share in the improvements made by the others. GPL redirects here. ... This article is about operating systems that use the Linux kernel. ... Free software is software that can be used, studied, and modified without restriction, and which can be copied and redistributed in modified or unmodified form either without restriction, or with minimal restrictions only to ensure that further recipients can also do these things. ...

Many real-life dilemmas involve multiple players. Although metaphorical, Hardin's tragedy of the commons may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). Such multi-player PDs are not formal as they can always be decomposed into a set of classical two-player games. The commons are not always exploited: William Poundstone, in a book about the Prisoner's Dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for someone to take a paper without paying (defecting) but very few do, perhaps feeling that if they do not pay then nor will others, destroying the system. (Because there is no mechanism for personal choice to influence others' decisions this widespread line of reasoning is called "magical thinking".)[9] Newspapers are less risky to distribute under the honour system than other consumables because taking more than one offers very little extra benefit. Another real-life example is gridlock. Garrett Hardin Garrett James Hardin (April 21, 1915 â€“ September 14, 2003) was a controversial ecologist from Dallas, Texas who was most known for his 1968 paper, The Tragedy of the commons. ... The Tragedy of the Commons is a type of social trap, often economic, that involves a conflict over resources between individual interests and the common good. ... William Poundstone is an American author, columnist, and skeptic. ... Excludability is defined in economics as whether or not it is possible to exclude people who have not paid for a good or service from consuming it. ... Causality or causation denotes the relationship between one event (called cause) and another event (called effect) which is the consequence (result) of the first. ... In psychology and cognitive science, magical thinking is non-scientific causal reasoning (e. ... The Honor System is a philosophical way of running a variety of endeavors based on trust and honor. ... In economics, diminishing returns is the short form of diminishing marginal returns. ... Gridlock is a term describing an inability to move on a transport network. ...

The theoretical conclusion of PD is one reason why, in many countries, plea bargaining is forbidden. Often, precisely the PD scenario applies: it is in the interest of both suspects to confess and testify against the other prisoner/suspect, even if each is innocent of the alleged crime. Arguably, the worst case is when only one party is guilty — here, the innocent one is unlikely to confess, while the guilty one is likely to confess and testify against the innocent. A plea bargain (also plea agreement, plea deal or copping a plea) is an agreement in a criminal case in which a prosecutor and a defendant arrange to settle the case against the defendant. ...

Related games

Closed-bag exchange

Hofstadter[10] once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange": Douglas Richard Hofstadter (born February 15, 1945 in New York, New York) is an American academic. ...

Two people meet and exchange closed bags, with the understanding that one of them contains money, and the other contains a purchase. Either player can choose to honour the deal by putting into his bag what he agreed, or he can defect by handing over an empty bag.

In this game, defection is always the best course, implying that rational agents will never play, and that "closed bag exchange" will be a missing market due to adverse selection. However, in this case both players cooperating and both players defecting actually give the same result, so chances of mutual cooperation, even in repeated games, are few. A missing market is a situation in microeconomics where a competative market allowing the exchange of a commodity would be Pareto-efficient, but no such market exists. ... Adverse selection or anti-selection is a term used in economics and insurance. ...

Friend or Foe?

Friend or Foe? is a game show that aired from 2002 to 2005 on the Game Show Network in the United States. It is an example of the prisoner's dilemma game tested by real people, but in an artificial setting. On the game show, three pairs of people compete. As each pair is eliminated, they play a game of Prisoner's Dilemma to determine how their winnings are split. If they both cooperate (Friend), they share the winnings 50-50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the payoff matrix is slightly different from the standard one given above, as the payouts for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If you know your opponent is going to vote Foe, then your choice does not affect your winnings. In a certain sense, Friend or Foe has a payoff model between "Prisoner's Dilemma" and "Chicken". Friend or Foe? is an American game show based on knowledge and trust, which aired on Game Show Network. ... GSN redirects here. ... The game of chicken (also referred to as playing chicken) is a game in which two players engage in an activity that will result in serious harm unless one of them backs down. ...

The payoff matrix is

Cooperate Defect 1, 1 0, 2 2, 0 0, 0

This payoff matrix was later used on the British television programmes Shafted and Golden Balls. Shafted was a British quiz show on ITV1, presented by Robert Kilroy-Silk. ... Golden Balls is a British daytime game show on the ITV Network, presented by Jasper Carrott. ...

A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... Extensive Form Representation of a Four Stage Centipede Game In game theory, the centipede game, first introduced by Rosenthal (1981), is an extensive form game in which two players take turns choosing either to take a slightly larger share of a slowly increasing pot, or to pass the pot to... Conflict resolution is any reduction in the severity of a conflict. ... In game theory, the Diners dilemma is an n-player Prisoners dilemma. ... In game theory, an evolutionarily stable strategy (or ESS; also evolutionary stable strategy) is a strategy which if adopted by a population cannot be invaded by any competing alternative strategy. ... In game theory, folk theorems are a class of theorems which imply that in repeated games, any outcome is a feasible solution concept, if under that outcome the players minimax conditions are satisfied. ... In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ... Neuroeconomics combines neuroscience, economics, and psychology to study how we make choices. ... The Price equation (also known as Prices equation) is a covariance equation which is a mathematical description of evolution and natural selection. ... In evolutionary biology, reciprocal altruism is a form of altruism in which one organism provides a benefit to another in the expectation of future reciprocation. ... The rendezvous dilemma is related to the prisoners dilemma and can be formulated in this way: Two young people have a date in a park they have never been to before. ... The concept of superrationality is discussed in Douglas Hofstadters book Metamagical Themas. Superrationality is based on the idea that two perfect logicians will come up with the same, correct, answer to a logical or mathematical problem. ... Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ... The Tragedy of the Commons is a type of social trap, often economic, that involves a conflict over resources between individual interests and the common good. ... The tragedy of the anticommons is a situation where rational individuals (acting separately) collectively waste a given resource by under-utilizing it. ... In game theory, the travelers dilemma (sometimes abbreviated TD) is a type of non-zero-sum game in which two players attempt to maximise their own payoff, without any concern for the other players payoff. ... Trust is the belief in the good character of one party, presumed to seek to fulfill policies, ethical codes, law and their previous promises. ... Social trap is a term used by psychologists to describe a situation in which a group of people act to obtain short-term individual gains, which in the long run leads to a loss for the group as a whole. ... In game theory the War of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while accumulating costs at a constant rate c. ... Zero-sum describes a situation in which a participants gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). ... Le Trou is a 1960 film directed by Jacques Becker. ... The Trap: What Happened to Our Dream of Freedom is a BBC documentary series by British filmmaker Adam Curtis, well known for other documentaries including The Century of the Self and The Power of Nightmares. ...

Notes

1. ^ A simple "tell" that partially or wholly reveals one player's choice — such as the Red player playing their Cooperate card face-up — does not change the fact that Defect is the dominant strategy. When one is considering the game itself, communication has no effect whatsoever. However, when the game is being played in real life considerations outside of the game itself may cause communication to matter. It is a point of utmost importance to the full implications of the dilemma that when we do not need to take into account external considerations, single-instance Prisoner's Dilemma is not affected in any way by communications.Even in single-instance Prisoner's Dilemma, meaningful prior communication about issues external to the game could alter the play environment, by raising the possibility of enforceable side contracts or credible threats. For example, if the Red player plays their Cooperate card face-up and simultaneously reveals a binding commitment to blow the jail up if and only if Blue Defects (with additional payoff -11,-10), then Blue's Cooperation becomes dominant. As a result, players are screened from each other and prevented from communicating outside of the game.
2. ^ Dawkins, Richard (1989). The Selfish Gene. Oxford University Press. ISBN 0-19-286092-5.  Page: 204 of Paperback edition
3. ^ Tversky, Amos (2004). Preference, Belief, and Similarity: Selected Writings. MIT Press. ISBN 026270093X.
4. ^ For example see the 2003 study “Bayesian Nash equilibrium; a statistical test of the hypothesis” for discussion of the concept and whether it can apply in real economic or strategic situations (from Tel Aviv University).
5. ^ The 2004 Prisoner's Dilemma Tournament Results show University of Southampton's strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (Note that in a PD tournament, the aim of the game is not to “win” matches — that can easily be achieved by frequent defection). It should also be pointed out that even without implicit collusion between software strategies (exploited by the Southampton team) tit-for-tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit-for-tat, but tit-for-tat is more robust). The same applies for the tit-for-tat-with-forgiveness variant, and other optimal strategies: on any given day they might not 'win' against a specific mix of counter-strategies.An alternative way of putting it is using the Darinian ESS simulation. In such a simulation Tit-for-Tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a Tit-for-Tat population is penetratable by non-retaliating nice strategies which in turn are easy prey for the nasty strategies. Richard Dawkins showed that here no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.
6. ^ Shy, O., 1996, Industrial Organization: Theory and Applications, Cambridge, Mass.: The MIT Press.
7. ^ a b This argument for the development of cooperation through trust is given in The Wisdom of Crowds , where it is argued that long-distance capitalism was able to form around a nucleus of Quakers, who always dealt honourably with their business partners. (Rather than defecting and reneging on promises — a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the meme for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general commerce
8. ^ Ward, D. (2004) The Program Manager's Dilemma The Program Manager's Dilemma (Defense AT&L, Defense Acquisition University Press).
9. ^ As well as being an explanation for the lack of petty-theft, magical thinking has been used to explain such things as voluntary voting (where a non-voter is considered a free rider). Potentially, it might be used to explain Wikipedia contributions: Text may be added under the assumption that if contributions are not made, then similar people will also fail to contribute (i.e. arguing from effect to cause). Alternatively, the explanation could depend on expected future actions (and not require a magical connection). Modelling future interactions requires the addition of the temporal dimension, as given in the Iterated prisoner’s dilemma section.
10. ^ Hofstadter, Douglas R. (1985). Metamagical Themas: questing for the essence of mind and pattern. Bantam Dell Pub Group. ISBN 0-465-04566-9.  - see Ch.29 The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation.

References

• Robert Aumann, “Acceptable points in general cooperative n-person games”, in R. D. Luce and A. W. Tucker (eds.), Contributions to the Theory 23 of Games IV, Annals of Mathematics Study 40, 287–324, Princeton University Press, Princeton NJ.
• Axelrod, R. (1984). The Evolution of Cooperation. ISBN 0-465-02121-2
• Kenneth Binmore, Fun and Games.
• David M. Chess (1988). Simulating the evolution of behavior: the iterated prisoners' dilemma problem. Complex Systems, 2:663–670.
• Dresher, M. (1961). The Mathematics of Games of Strategy: Theory and Applications Prentice-Hall, Englewood Cliffs, NJ.
• Flood, M.M. (1952). Some experimental games. Research memorandum RM-789. RAND Corporation, Santa Monica, CA.
• Kaminski, Marek M. (2004) Games Prisoners Play Princeton University Press. ISBN 0-691-11721-7 http://webfiles.uci.edu/mkaminsk/www/book.html
• Poundstone, W. (1992) Prisoner's Dilemma Doubleday, NY NY.
• Greif, A. (2006). Institutions and the Path to the Modern Economy: Lessons from Medieval Trade. Cambridge University Press, Cambridge, UK.
• Rapoport, Anatol and Albert M. Chammah (1965). Prisoner's Dilemma. University of Michigan Press.
• Le, S. & Boyd, R. (In press). Evolutionary dynamics of the continuous iterated Prisoner's Dilemma, Journal of Theoretical Biology Full text
• A. Rogers, R. K. Dash, S. D. Ramchurn, P. Vytelingum and N. R. Jennings (2007) “Coordinating team players within a noisy iterated Prisoner’s Dilemma tournament” Theoretical Computer Science 377 (1-3) 243-259. [2]

Israel Robert John Aumann (×™×©×¨××œ ××•×ž×Ÿ) (born June 8, 1930) is an Israeli mathematician and a member of the United States National Academy of Sciences. ... Robert Axelrod is the Arthur W. Bromage Distinguished University Professor of Political Science and Public Policy at the University of Michigan. ... The Evolution of Cooperation is a 1984 book and a 1981 article of the same title by political science professor Robert Axelrod. ... Kenneth G. Binmore (born August, 1940) is a well-known economist and game theorist. ... Melvin Dresher was a mathematician, notable for developing, with Merrill Flood, the game theoretical model of cooperation and conflict known as the Prisoners dilemma while at RAND in 1950. ... Merrill Meeks Flood was a mathematician, notable for developing, with Melvin Dresher, the basis of the game theoretical Prisoners dilemma model of cooperation and conflict while at RAND in 1950 (Albert W. Tucker gave the game its prison-sentence interpretation, and thus the name by which it is... The RAND Corporation is a nonprofit global policy think tank first formed to offer research and analysis to the United States armed forces. ... The headquarters of the Cambridge University Press, in Trumpington Street, Cambridge. ... This article is about the city in England. ... Anatol Rapoport (born May 22, 1911) is a Russian-born American Jewish, mathematical psychologist. ... The University of Michigan Press is a publisher and part of the University of Michigan. ...

• Plous, S. (1993). Prisoner's Dilemma or Perceptual Dilemma? Journal of Peace Research, Vol. 30, No. 2, 163-179.

Results from FactBites:

 Hobbes and the Prisoner's Dilemma (2490 words) The situation in Hobbes' state of nature is like the Prisoners' Dilemma: By acting solely on self-interest, you and the other people end up in a situation that is worse for everyone than an alternative possible outcome that you could have reached. What makes this a prisoner's dilemma is that no matter what B does, A is better off preparing; and whatever A does, B is better off preparing. In the original prisoners' case in which the prisoners are allowed to confer and make promises, if we imagine that this situation happens again and again, getting busted on, say, drug-possession charges, where the penalties are in days rather than years, criminals will get reputations for keeping promises or violating them.
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