Cheaters Never Prosper? Why The Prisoner's Dilemma Is Not As Simple As You Think

That was all Bob could think as he sat in his cell. The plan should have worked, and it didn’t, and now he and his partner-in-crime Alice were being kept in separate rooms, unable to see or communicate with each other as the cops interrogated them about the robbery.

Of course, he knew they didn’t have enough evidence to lock them both up. No, it was almost worse – for the charges to stick, they needed a confession. So, a couple of hours ago, they’d offered Bob a deal: sell out Alice, and he’d go free. Alice, on the other hand, would face a year in jail.

Keep schtum, they warned, and he’d be detained without charge for as long as they could hold him – maybe a month or more. And they’d not been shy about telling him the flipside of that little offer: they’d given Alice the exact same choice. She was mulling it over right now – hell, she might have ratted him out already.

And the kicker? If both of them turned on each other, then they’d both go down. Only for nine months – less than if they said nothing and their partner sang – but still. Bob didn’t want to go down at all if he could help it.

So… what should he do?

What is the Prisoner’s Dilemma?

You might recognize the scenario above. It’s the classic Prisoner’s Dilemma, designed in 1950 by mathematicians Merrill Flood and Melvin Dresher and now one of the poster children of the entire field of game theory.

It’s also… kind of depressing.

“This is the standard conclusion of the Prisoner's Dilemma: the two characters will betray one another,” explained economist and data scientist Lucas Husted in a 2020 TED-Ed video on the thought experiment.

“Their strategy to unconditionally sacrifice their companion is what game theorists call the ‘Nash Equilibrium’,” he said, “meaning that neither can gain by deviating from it.”

The reasoning is simple: set out the payoff matrix for the problem, and we see that whatever Alice chooses to do, Bob gets a lighter punishment if he betrays her.

The logic is inarguable, even if the conclusion is unsatisfying. “[Its] reward structure forces interacting agents to either become cheaters or die off in the course of evolution,” explains Alexandre Morozov, a professor in the Department of Physics and Astronomy at the Rutgers School of Arts and Sciences. “[And] cheaters always act as cheaters: with respect to the other members of the population, [even] their own progeny.”

This holds up even if you do the experiment more than once, by the way. Think about it: if you’re going to do the Prisoner’s Dilemma even just twice in a row, then whatever happens before the final round doesn’t matter that much – sure, you might stay loyal to me today, but what’s to stop you ratting me out tomorrow? At that point, I may as well rat you out today, which means you should probably rat me out today as well, and, well, you get the idea.

There’s just one problem, really, and it’s this: if turning on your compatriots is always the best option… then why are we all here?

A case for optimism

As evocative as the Prisoner’s Dilemma is, it’s really not all that true-to-life. “[In] real-life situations like trade negotiations and international politics[,] [r]ational leaders must assume that the decisions they make today will impact those of their adversaries tomorrow,” pointed out Husted.

If you’re thrown into the Prisoner’s Dilemma with no fixed endpoint, we have what’s known as the Iterated Prisoner’s Dilemma – and it’s here that the problem starts feeling more grounded. “Selfishness may win out in the short-term,” Husted said, “but with the proper incentives, peaceful cooperation is not only possible, but demonstrably and mathematically ideal.”

The current view that cooperators will always yield to absolute cheaters, leading to the societal collapse, is perhaps too pessimistic.

Alexandre Morozov

You can prove this theoretically, but you don’t need to. Back in the late 1970s, Robert Axelrod, a professor of political science at the University of Michigan, set up an international tournament to figure out exactly which tactics are best for “winning” the Dilemma. 

It took 2,100 rounds of head-to-head matches between individual algorithms from psychologists, economists, mathematicians, and more; more than a day of processing on the university’s state-of-the-art room-sized computers; the final tally was done by hand, and the results – well, they were unexpected.

“Having based my expectations on computer chess, I was surprised that the winner was the simplest of all the strategies submitted,” Axelrod would later write. Named “Tit for Tat”, it was a tiny little thing, sent in by somebody better known for his work in peace theory than battle royales: Anatol Rapoport.

“Tit for Tat begins with cooperation,” Axelrod explained, “and then, as the name implies, simply does what the other player did on the previous move.” In other words: it rewards opponents who are loyal, but swiftly punishes those who betray. And this, it turned out, was the key to its success: “Tit for Tat won the tournaments even though it could never do better than the player it was interacting with,” Axelrod pointed out. “Instead it won by […] eliciting cooperation.”

Time and again, the strategy of being “nice” – that’s a technical term, genuinely – beat out more ingenious and more complex algorithms. It seems cooperation is stronger after all – and in the years since, research has borne that out even further.

“In a scenario which is slightly more realistic than the classical Prisoner's Dilemma, cooperation can arise and will be maintained,” Morozov told IFLScience. “So, the current view that cooperators will always yield to absolute cheaters, leading to the societal collapse, is perhaps too pessimistic.”

Outwitting the odds

Why should cooperation beat selfishness, when it’s the latter that ought to pay off? Perhaps, you might think, the answer is obvious: we’re not mathematical formulae, are we? We’re humans – intelligent beings and, nominally at least, rational actors.

Cooperation, in most instances, is a rational choice.

Eugenio Proto

To a certain extent, that’s true. Back 2019, a team of economists ran the Prisoner’s Dilemma again, this time sorting the players into groups based on certain personality or cognitive traits: how pro-social they were; how conscientious; how intelligent. And one of those characteristics proved crucial to predicting how participants would play: “Overall, we found that the higher a person’s intelligence, the more cooperative they became as they continued playing the Prisoner’s Dilemma game,” the team wrote in an accompanying article for The Conversation at the time.

“So while intelligent individuals are not inherently more cooperative, they have the ability to process information faster and to learn from it.”

It's a tempting conclusion: that we, through our human intelligence, can transcend even the universal truth of mathematics. But in truth, none of that brainpower is necessary – all you need is the ability to remember a face.

That’s the finding from a new paper by Morozov and his coauthor, Hebrew University of Jerusalem physicist Alexander Feigel. “In our model, the reward structure is the same as in the classical setup,” Morozov tells IFLScience. There’s just one difference: “individuals are free to act as cheaters with some members of the population, while cooperating with others.”

Exactly how opponents are sorted into either group is entirely random – no information about individuals’ reputations or similarity to the player is required, as other studies have sometimes relied on. “All you have to do is remember who you interacted with and react in the same way,” Morozov explained in a statement last week. “That’s enough for cooperation to emerge by itself in many scenarios. It’s what physicists call an emergent property.”

It's not all peace and love: set up a society with Morozov and Feigel’s instructions, and you’ll see periods of stability interrupted by upheaval and extinctions. “This is because being a cheater is now relative,” Morozov tells IFLScience. “Subpopulations can get boosted by cheating, driving too-cooperative members of another subpopulation into extinction.”

“However, the members of the now-dominant subpopulation are actually better off at this stage if they cooperate with one another,” he explains. “In most cases, they outcompete absolute cheaters.”

Nice guys… last

There’s a reason the Prisoner’s Dilemma has proved so popular for so long: it “capture[s] the essence of the tension between doing what is good for the individual,” mused Axelrod, “and what is good for everyone.”

Of course, there’s no definitive “best” way to solve the Dilemma – there probably never will be, as each game is individual to the players, information, and conditions specified. “We expect our work to be the first in a series of papers, written by us or perhaps by others,” Morozov tells IFLScience, “which will explore opponent-specific flavors of various evolutionary games.”

Their small modification to the design may have made the Dilemma “more realistic,” he says, but there are many further refinements that might be added: “studying spatially structured populations, for example,” he suggests, “or evolutionary outcomes in smaller populations, where the stochastic nature of reproduction […] plays a major role comparable to that of selection and mutation.”

Nevertheless, after decades of research, thought experiments, mathematical modeling, and thousands-strong tournaments, it seems the best answer for how to beat the Prisoner’s Dilemma is… well, more or less what you’d expect: that, while being selfish might pay off immediately, cooperation is the better tactic long-term.

“Cooperation, in most instances, is a rational choice,” advises Eugenio Proto, a professor of economics at the University of Glasgow and coauthor of the 2019 paper connecting the Prisoner’s Dilemma to intelligence. “[It] can be naturally sustained because many interactions in life are repeated.”

“We simply need to be intelligent and wise enough to recognize this,” he tells IFLScience, “and resist the temptation to pursue myopic, short-term gains.”

The new study is published in the journal PNAS.