GAME THEORY- THE PRISONER’S DILEMMA

The prisoner’s dilemma is a standard example of a game analyzed in 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 Flood and Dresher in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it “prisoner’s dilemma” -Poundstone, 1992, 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. They hope to get both sentenced to a year in prison 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 offer situation is:

• If Prisoner 1 and Prisoner 2 each betray the other, each of them serves 2 years in prison

• If Prisoner 1 betrays Prisoner 2 but Prisoner 2 remains silent, Prisoner 1 will be set free and Prisoner 2 will serve 3 years in prison (and vice versa)

• If Prisoner 1 and Prisoner 2 both remain silent, both of them will only serve 1 year in prison -like the lesser charge.

The prisoners´s dilemma in movies

Sandra Bullock’s “Murder by Numbers,” a laborious, visually gloomy and generally distasteful police procedural.

Sandra Bullock stars as a hard-bitten homicide detective. At first, the casting of the normally adorable Bullock (who was rightly voted “Most Likely To Brighten Up Your Day” in high school) as a callous, embittered cop seems bizarre. Eventually, though, we learn that she’s such a tough cookie only because she was brutally assaulted as a teen, and that if she would simply learn to face her fear of her abuser, she could get back in touch with her inner cutie-pie. That’s a subplot, however. In fact, the two little-known actors playing the murderers get as much screen time as the star. The film is structured like an old “Columbo” episode, with Bullock in the Peter Falk role, tracking down the smug 18-year-olds whom the audience already knows are the killers.

“What had this boy (Loeb) to do with it?” “He was not his own father; he was not his own mother … All of this was handed to him. He did not surround himself with governesses and wealth. He did not make himself. And yet he is to be compelled to pay.”

Nihilistic assault on the concepts of personal responsibility and justice itself was long celebrated as the ultimate condemnation of the death penalty. Times have changed, though. Thus, “Murder by Numbers” makes only cursory efforts to drum up sympathy for Pitt’s Loeb character. Lacking enough evidence to arrest the pair, Bullock and her long-suffering partner realize their only hope is a confession. They place Gosling and Pitt into separate rooms and tell each that whoever first implicates the other as the one who actually stabbed the woman will live, while the one who stays silent will die in the gas chamber.

This is a classic rendition of the “Prisoner’s Dilemma,” which fascinates the kind of game theorists we met in “A Beautiful Mind.” Implicit in the Prisoner’s Dilemma, however, is that if the two suspects stay loyal to each other, they will both walk. Because the movie hasn’t yet told us who had held the murder weapon, this makes for the dramatic high point of the film.

The prisoner’s dilemma can also work without the death penalty, but only if the accomplice’s sentence is much milder than life in prison. It’s the large gap between the two punishments that gives Gosling and Pitt an incentive to squeal on each other.

It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other.[1] The interesting part of this result is that pursuing individual reward logically leads both of the prisoners to betray when they would get a better reward if they both kept silent. In reality, humans display a bias systemic towards cooperative behavior in this and similar games despite what is predicted by simple models of “rational” self-interested action.

An extended “iterated” version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner’s dilemma tournaments have been held to compete and test algorithms for such cases.

The prisoner’s dilemma game can be used as a model for many real world situations involving cooperative behavior. In casual usage, the label “prisoner’s dilemma” may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activities.

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