Looking in horror at the current—and seemingly interminable—bloodletting between Israelis and Palestinians, the problem seems frustratingly simple: Why don’t they just cooperate? as Rodney King famously asked after he had been beaten by police in Los Angeles: Why can’t we all just get along?

The answer turns out to be more complex than one might think, and not merely in the Middle East. Some insight can be gained by turning to game theory, a decision-making technique widely used by economists, mathematicians, strategic analysts, psychologists, political scientists and even biologists (and about which I wrote a book some time ago: The Survival Game: how game theory explains the biology of cooperation and competition, Henry Holt, 2003). Although game theory helps illuminate such problems—and thus contributes to clarifying our thinking—it is unfortunately less clear about how to solve them. Indeed, as we’ll see, it’s limited in how much insight it actually provides, but is worth understanding nevertheless, if only because game theory is great intellectual fun and—more importantly—it is widely consulted by those who make important decisions.

In its simplest cases, game theory is a way of looking at situations involving two sides who interact, as a result of which each receives a “payoff” determined not merely by what it does, but by the other’s behavior, too. This is extremely important: Usually, it isn’t terribly challenging to identify the “best” behavior so long as one’s choice is not somehow influenced by and simultaneously likely to influence, in turn, what another “player” does. If it is raining, the decision of whether or not to carry an umbrella is relatively easy, especially since that decision isn’t likely to effect whether or not it will rain. But what about the decision of whether or not to cooperate with someone else, when your payoff—and that of the other side—depends on what you and your partner/opponent choose? And, moreover, each of you knows that, and is liable to adjust her behavior accordingly.

Unfortunately, situations of this sort frequently impede cooperation, especially when each player fears being exploited by the other. Especially prominent—and relevant to the deadly Israeli-Palestinian embrace—is one long recognized, and modeled mathematically, as the Prisoner’s Dilemma; henceforth, PD. (I have written about a peculiar three-person game and also about the other well-known game, the so-called Game of Chicken, as a useful metaphor for conceptualizing Democratic-Republican struggles over the budget ceiling. Sadly, the prospect arises yet again with respect to the looming “fiscal cliff.”)

During times of international tension, participants are likely to be acutely suspicious that the other side is dangerous, and likely to probe for weakness, being deterred only by strength, During the Cuban Missile Crisis and the Vietnam War, White House aides argued that the Soviets were following the Leninist maxim, “If you strike steel, pull back; if you strike mush, keep going.” And, of course, so long as each side is determined to meet the other with steel rather than mush, each can justify its policy by pointing to the other.

In the admittedly over-simplified thought-experimental world of PD, each participant has two options: “cooperate” (e.g., be nice, mush, etc.) vs “defect” (e.g., be nasty, steel, etc.). If both cooperate, each receives a Reward for doing so; if both defect, each receives a considerably lower payoff, the Punishment of mutual defection, But if one defects and the other cooperates, the defector gets the highest payoff of all, called the Temptation to defect, and the one who cooperates while the other takes advantage of the situation receives the lowest, Sucker’s payoff.

A PD occurs when payoffs are in the following relationship: Temptation > Reward > Punishment > Sucker. In this case, each side is motivated to obtain the highest payoff (Temptation) and fearful of getting stuck with the lowest (Sucker). To understand what happens next, imagine yourself inside the head of either player, trying to decide how to behave: “The other side might cooperate with me or defect. If she cooperates, then my best move is to defect, since then I would get highest payoff of all (Temptation). On the other hand, she might defect, in which case my best move—once again—is to defect, because even though I get the Punishment, which admittedly is a poor payoff, at least its better than ending up a Sucker.”

Each player is therefore moved to defect, which presents a troubling dilemma indeed, since by doing so they each get the Punishment of mutual defection (a debilitating arms race, or, in today’s Middle East, repeated episodes of murder and mayhem), when the best mutual payoff by far would have been the shared Reward for cooperation or at least, mutual restraint.

The Prisoner’s Dilemma is a useful way of modeling the dilemma of thinking one must be “nasty” for fear that anyone who is “nice” is at the mercy of others who persevere in being nasty. On the other hand, it is also unduly pessimistic in that it assumes only two choices whereas in reality, individuals or states have a variety of intermediate options, known to statesmen as “confidence building measures.” Similarly, PD also requires that its “games” are one-time affairs, although in reality, states interact many times in succession, and can therefore vary their behavior depending on what happened the previous time. When both sides have an interest in generating a sequence of cooperative interactions, being nice isn’t merely for saints, softies or suckers: It can yield the highest payoff for everyone concerned.

Computer models have shown, in fact, that when two players have the prospect of continued future interactions, even a deadly PD can be resolved in favor of mutual cooperation, in which both sides are rewarded for cooperation. Optimum tactics depend on variations on the well-known technique of “tit-for-tat,” made famous by University of Michigan political scientist Robert Axelrod.

Because of simple geography if nothing else, and despite the deluded claims of extremists on each side, Israelis and Palestinians are stuck with a long, shared “shadow of the future,” in which they will either live together or die together. On the other hand, the Israeli-Palestinian standoff departs from classic PD in other respects as well, notably the fact that the theory requires that both sides be otherwise balanced such that costs and benefits are symmetrical. The current situation, however, is distinctly unbalanced, with Israel having a massive military and economic advantage; moreover, many—perhaps most—Israelis are more or less content with the current socio-economic and political situation, whereas the overwhelming majority of Palestinians are not. Hence, the latter are strongly disposed to depart from a stale-mate, engaging in actions that appear—to Israelis and many Americans—as defecting, whereas from the Palestinian perspective, the current status quo is one in which Israel is chronically defecting while the Palestinians languish as Suckers.

Game theory helps clarify the dilemma of 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, if they can be persuaded to take a wider view of their situation and, thus, their opportunities.

David P. Barash is professor of psychology at the University of Washington; his most recent book is Homo Mysterious: evolutionary puzzles of human nature (2012, Oxford University Press)

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