01 March 2009

The Prisoner’s Dilemma and Other Opportunities

By David P. Barash

Game theory suggests that, although it is not at all simple to accomplish, cooperation can often be shown to be preferable to conflict.

David P. Barash is a professor of psychology at the University of Washington and co-author of Peace and Conflict Studies, among many other books.

This article appears in the March 2009 issue of eJournal USA, Nonviolent Paths to Social Change (PDF, 783 KB).

The problem seems simple enough: Why don’t people cooperate? Or at least, why don’t they cooperate more than they currently do? After all, if I helped you and in return you helped me, wouldn’t both of us be better off? Similarly, wouldn’t everyone benefit if we all followed the path of nonviolence? In short, what is so difficult about the question famously posed by U.S. motorist Rodney King after he had been beaten by police in Los Angeles: Why can’t we all just get along? Nonviolently.

The answer turns out to be more complex than one might think. Moreover, a series of decision-making techniques known as game theory helps illuminate both the problems — including the problem of violence versus nonviolence — and some strategies for solving them.

Game theory, in brief, is a way of looking at situations involving, in the simplest case, two sides (or “players”), with “payoffs” or “outcomes” determined not merely by what a given player does, but by the interaction of both sides involved. Without this interaction component, such “games” wouldn’t be very difficult: Each player would simply do whatever it takes to get the best outcome for himself or herself, regardless of the other player. For example, if it is raining, the correct “move” may be to carry an umbrella, regardless of what the other does. The weather is unlikely to be influenced by anyone’s behavior; each is therefore free to follow his or her inclinations, without regard to the other’s course of action.

On the other hand, imagine that two people discover, say, a small pile of money. They will likely be best served by taking the other into account: for example, dividing the loot rather than each trying to monopolize the payoff and possibly fighting over it as a result. It is when payoffs are determined not just by what individual A does, but also by what B does simultaneously, that game theory is called for.

Unfortunately, however, such decisions are often less straightforward than merely splitting the difference, and, worse yet, they frequently provide occasions for noncooperation, especially when cooperation by one player renders him vulnerable to being exploited by the other. Such situations, of course, are often encountered by individuals and social groups seeking to prevent conflict and avoid violence.

In short, there is an ever-present risk that, by choosing cooperation over competition, nonviolent practitioners risk losing out to those who are more aggressive and violence prone. Imagine, for example, that in the case of two people discovering a pile of money, one elects to pull out a gun and claim the money as his, while the other is committed to nonviolence. The inevitable result would appear to be that the violent participant is rewarded for his behavior (he gets the money), while the nonviolent one is left empty-handed. Or as Machiavelli famously put it, “A man who wishes to make a profession of goodness in everything must necessarily come to grief among those who are not good.”

Nonviolent Solutions

But there is hope, as well: Game theory not only helps us understand the problem, but also suggests and supports nonviolent solutions.

The Prisoner’s Dilemma, derived from game theory, is a model for the evolution of cooperation versus competition more generally. Like most models, it is overly simple, but it helps clarify one’s thinking.

Assume that two individuals — or groups, or even states — both have the choice of being either nonviolent or violent. (Theorists generalize these options to “cooperate” versus “defect” or “nice” versus “nasty,” including such international matters as arms races and the imposition of trade barriers.) If both parties choose nonviolence, each receives a reward for doing so: peacefully resolving their dispute or, in the case of found money, obtaining a share without fighting. If both choose violence, each receives a different payoff: the punishment of possible injury. But if one defects and the other cooperates, the violent defector gets what is called the temptation to defect (all the money in this example), and the one who cooperates (who behaves nonviolently while the other chooses violence) receives the sucker’s payoff: no money in this example.

To understand what happens next, imagine yourself inside the head of either player: “The other fellow could either cooperate with me (be nonviolent) or defect. If the former, then my best move is to threaten violence because then I would get the highest payoff of all while he — a sucker — would get nothing. On the other hand, he might choose to defect and threaten violence, in which case my best move — once again — is to do the same, because even though I get the punishment of a possible fight, which admittedly is a poor payoff, at least it’s better than ending up a sucker and losing out altogether.”

The result of this strict logic is that each side is inclined to possibly violent defection, which presents a troubling dilemma indeed because, by doing so, each gets a punishment (in the case of individuals, a fight, or in the case of nations, perhaps a debilitating arms race or trade war) when the best mutual payoff would have been the shared reward for cooperation and nonviolence.

 

The Prisoner’s Dilemma is a useful way of modeling this dilemma, thinking that one must be nasty for fear that anyone who is nice is at the mercy of others who persevere in being nasty (recall Machiavelli).

On the other hand, it isn’t the only way of looking at such situations. For example, when it comes to violence and nonviolence, a more appropriate model may well be the so-called game of Chicken, which resembles Prisoner’s Dilemma except that here, punishment is the worst payoff of all: The cost of mutual fighting — or even threatening to fight — exceeds the cost of being a sucker and avoiding conflict altogether. Chicken is a “game” in which two drivers drive toward each other on a collision course, with each seeking to induce the other to swerve. The one who swerves — equivalent to cooperating in Prisoner’s Dilemma — is considered to be a “chicken” (slang for coward), whereas the one who goes straight –- equivalent to defecting in Prisoner’s Dilemma –- wins. The problem, however, is that if each player is determined to defect, and thus to win at the other’s expense, the result is that both lose!

Repeated Rounds

Simplified game theory models also assume that there is only one possible payoff and that any interaction is a one-time affair. But in reality, individuals and groups often interact repeatedly, and they can vary their behavior depending on what happened the previous time. Both sides therefore have a genuine interest in generating a sequence of nonviolent, cooperative interactions because, whether Prisoner’s Dilemma or a game of Chicken, the reward of nonviolent cooperation is always higher than the punishment of mutual violence. Therefore, such outcomes can indeed yield the highest payoff for everyone concerned.

Interestingly, even in isolated, one-time interactions, when a strictly rational calculation suggests that competitive defection is the “logical” response, most people are inclined to attempt cooperation, especially when they understand that the interaction in question will likely be repeated. Continued interactions offer not only the potential downside of repeated punishments for mutual defection (violence), but also the prospect of enjoying continuing rewards from shared cooperation (nonviolence).

Mathematical and computer-based simulations have shown, for example, that a simple strategy of tit-for-tat can generate the highest payoff of all, even in a classic Prisoner’s Dilemma situation. Such a strategy involves initial cooperation, after which each player merely repeats the move employed by the other in the previous round. Thus, cooperation by player A engenders cooperation by player B indefinitely — as a result of which, both obtain the repeated reward of nonviolent cooperation. By the same token, defection by A produces defection by B, thereby protecting B from being suckered more than once and, in the process, discouraging A from defecting in the first place.

Mohandas Gandhi did not condone tit-for-tat retaliation, but he strongly emphasized that satyagraha — his term for active nonviolence — must be distinguished from passive acquiescence or the desire to avoid conflict at any price. He was also quite clear that by their actions, satyagrahis eventually modify the behavior of would-be defectors, that by their example and willingness to accept suffering (to be occasional suckers, in game theory terminology), they can do something that game theorists do not usually consider: change the behavior of the other party by appealing to his or her higher nature.

When a victim responds to violence with yet more violence, he or she is behaving in a manner that is predictable, perhaps even instinctive, which tends to reinforce the aggression of the original attacker and even, in a way, to vindicate the original violence, at least in the attacker’s mind. Since the victim is so violent, presumably he or she deserved it! Moreover, there is a widespread expectation of countervailing power analogous in the social sphere to Newton’s First Law, which states that for every action there is an equal and opposite reaction. Thus, if A hits B and then B hits back, this nearly always encourages A to strike yet again. Gandhi was not fond of the biblical injunction “an eye for an eye, a tooth for a tooth,” pointing out that if we all behaved that way, soon the whole world would be blind and toothless.

Instead, if B responds with nonviolence, this response not only breaks the chain of anger and hatred (analogous to the Hindu chain of birth and rebirth), but also puts A in an unexpected position. “I seek entirely to blunt the edge of the tyrant’s sword,” wrote Gandhi, “not by putting up against it a sharper-edged weapon, but by disappointing his expectation that I would be offering physical resistance.” Such resistance is neither easy nor likely to be painless, but game theory, as well as the practical experience of Gandhi in South Africa and India and of Martin Luther King Jr. and other activists in the United States, confirms that it can be spectacularly successful.

The ancient Roman statesman and philosopher Cicero, in Letters to His Friends, asked, “What can be done against force, without force?” Students of nonviolence would answer, “plenty.” Moreover, they would question whether anything effective, lasting, or worthwhile can be done against force, with force. After all, as we have seen, mutual recourse to violence readily leads to what game theorists identify as the punishment of mutual defection, to the detriment of all. American civil rights leader King, who, like Gandhi, was also intensely practical and result oriented, wrote that “returning violence for violence multiplies violence, adding deeper darkness to a night already devoid of stars. Darkness cannot drive out darkness; only light can do that. Hate cannot drive out hate; only love can do that.”

In summary, game theory helps illuminate the limits to cooperation, revealing why “getting along” isn’t as simple — or even as natural — as many would wish. But at the same time, it shows that human beings aren’t necessarily doomed to a Hobbesian world of endless, punishing defection and painful competition if they can be persuaded to take a wider view of their situation and, thus, their opportunities.

The opinions expressed in this article do not necessarily reflect the views or policies of the U.S. government.