Prisoner’s Dilemma and Mutual Cooperation
Understanding mutual cooperation is a key element in studying how people work together. Mutual reciprocity is seen everywhere: friends doing favors for each other, animals sharing food or helping one another, and nations coordinating joint policies. All of these interactions follow the rules of cooperation. Such cooperation requires people to be willing to help others, but also to stand up for themselves when exploited. So, what rules can ensure that cooperation is successful and mutually beneficial, rather than selfish and exploitative?
To explore this question, Charlotte Rossetti and Christian Hilbe from the Max Planck Institute for Evolutionary Biology, together with colleagues from Dalian University of Technology (China), used the so-called repeated prisoner’s dilemma.
The Repeated Prisoner’s Dilemma
In the repeated prisoner’s dilemma, two players simultaneously face the same choice: pay a small cost to give the other player a financial benefit, or do nothing. Ideally, both players should “cooperate” and pay this cost so that both benefit. However, there is always the risk that one player will avoid paying and take advantage of the benefit given by the other.
How can we play in a way that allows for cooperation while limiting selfish behavior?
The “Tit for Tat” Strategy and Its Limitations
A typical approach to the repeated prisoner’s dilemma is the “tit for tat” strategy. In a society where people use “tit for tat,” cooperation can develop and thrive, but there is a major drawback: when people make mistakes, mutual cooperation becomes unstable.
“Tit for tat is a good rule of thumb, easy to implement, and feels very human. After all, it’s based on an old saying,” says Charlotte Rossetti. “But it’s not forgiving enough and doesn’t account for mistakes, which we know are all too common among people. If I genuinely want to cooperate but make a mistake, I can only cooperate again when the other side also makes a mistake, so we even the score.”
Cumulative Reciprocity (CURE)
To address these shortcomings, the researchers analyzed an alternative strategy they called “cumulative reciprocity,” or CURE. People using CURE track the imbalance of cooperative actions in their interactions. This means that in each round, they observe whether both players have cooperated equally often in the past, or if the relationship is skewed in favor of one player. If the imbalance is zero or low enough, the strategy suggests cooperating. However, if the imbalance becomes too large, there is a risk of being exploited, and the strategy then suggests acting selfishly.
The first advantage of the CURE strategy is practical. By calculating a simple number (the current imbalance), people can consider the entire interaction process without having to remember the outcome of every round in detail. This greatly simplifies calculations and allows researchers to thoroughly analyze the model.
The team led by Hilbe and Xia studied the mathematical properties of this strategy and conducted large-scale computer simulations. They used these to test how cooperation develops in different environments. The results show that CURE can promote fairness while allowing for mistakes. It is also able to defend itself in hostile environments.
Predicting Human Behavior
Another advantage of CURE is its intuitiveness and simplicity, which makes it possible to predict real human behavior.
To study this aspect in more detail, Charlotte Rossetti conducted an online experiment where participants could play with another person for a small amount of money. The results show that CURE explains participants’ decisions better than other rules, especially when the experiment simulates human errors. The fact that people sometimes make mistakes when interacting with others can be devastating for cooperation. Therefore, any model aiming to accurately reproduce human behavior must take this into account.
Psychologists know that in friendships and other close relationships, most people do not keep exact records of who owes what to whom. Instead, they have a general sense of whether the relationship is fair or not. CURE perfectly captures this behavior.
Interestingly, this approach does not require people to consciously choose such a strategy. Strategies like CURE can naturally emerge over time, turning into simple rules of the game. These rules then promote mutual cooperation.