The True Story of the Birth of the Prisoner's Dilemma
It Was Born as Riveting Tale of Cooperation
The Prisoner's Dilemma, a famous concept in game theory, is often used to illustrate how individualistic incentives can sabotage collective gains. Yet, I present in my book "Optimally Irrational," a lesser-known but riveting tale that shows us a different side of this paradox.
The Prisoner's Dilemma is a story used in economics and game theory to highlight that cooperation can be hard to sustain. It presents a hypothetical scenario where two individuals are arrested for a crime and held in separate cells. They cannot communicate with each other and must make a decision independently - to confess or stay silent.
If both stay silent, they serve a short sentence (for example, one year) due to lack of evidence. If both confess, they serve a longer sentence (for example, five years), but less than they would if one confesses and the other doesn't. If one confesses and the other stays silent, the one who confesses goes free, while the other gets the longest sentence (for example, twenty years).
Despite the fact that both would be better off if they both remained silent, individual logic dictates that they confess. This is because, without knowing what the other will do, each prisoner faces a choice between a possible light sentence (if they confess) or the harshest sentence (if they stay silent and the other confesses). As such, the individually rational decision is to confess. This leads to a collectively undesirable outcome, where both confess and receive a harsher punishment than if they had cooperated and stayed silent. The crux of the dilemma lies in the fact that both prisoners would ideally prefer mutual cooperation and silence; however, their individual rationality inevitably drives them to defect and confess.
This scenario is often used to illustrate the difficulties of achieving cooperative behaviour in situations where individual and collective interests conflict. It is within this context that the story of the first-ever Prisoner's Dilemma experiment, conducted by Merrill Flood and Melvin Dresher, unfolds.
The story takes us back to January 1950 when two RAND corporation scientists, Merrill Flood and Melvin Dresher, set up the first-ever behavioural experiment of what would later be called the Prisoner's Dilemma. They invited economist Armen Alchian and mathematician John Williams to participate in a hundred-round game, where each round’s payoffs generated the dilemma’s quandary.
What ensued was a fascinating dance of decision-making, illuminating the potential for cooperation in social interactions. Instead of an endless cycle of defections, as the one-shot theory would predict, cooperation emerged as the primary strategy, occurring 60% of the time. Mutual defection, on the other hand, occurred a mere 14% of the time.
Alchian and Williams' recorded comments provide an intriguing window into their strategies as the game progressed. Williams, ever hopeful, initially chose to cooperate, noting, "Hope he's bright." On the other hand, the economist Alchian defected, baffled by his counterpart's decision, and exclaimed, "What is he doing?!!"
Over time, their dynamic evolved. Williams, determined to enlighten Alchian, alternated between punishment and opportunity - defection and cooperation. His strategy bore a striking resemblance to the "Tit for Tat" approach, which has since become a cornerstone in understanding sustained cooperation in repeated games. His comments during this period were quite telling: “This is like toilet training a child, you have to be very patient.” Alchian, initially expecting mutual defection, gradually grasped the undercurrents of Williams' actions, asking himself, “Is he trying to convey information to me?” This realization led him to cooperate most of the time, providing an unexpected, yet heartening twist to the tale.
This transformation from expected defection to prevalent cooperation, mirrored David Hume's wisdom from 1739, "I learn to do service to another, without bearing him any real kindness; because I foresee, that he will return my service, in expectation of another of the same kind." In layman's terms, "You scratch my back, I scratch yours."
John Nash, when asked about the results, suggested that repeated games have more rational strategies than just playing the single-game strategy (defection) repeatedly. This was later formalized as the Folk Theorem, stating that infinitely repeated games can yield payoffs from sustained cooperation. The reason? The looming threat of losing the gains from future cooperation deters present defection. Consider the “grim strategy”, It begins with cooperation and continues as long as the other player reciprocates. But if the other player defects, it switches to permanent defection. When both players adopt this strategy, they become entrenched in a cooperative equilibrium, with neither having an incentive to defect, as doing so would eliminate all the possible gains from future collaborative interactions.
This compelling story throws light on the profound implications of the Folk Theorem. It establishes that sustained cooperation isn't irrational but can emerge naturally among self-interested individuals if the probability of future interactions is high. This overturns the typical description of traditional economic theories that suggests systematic uncooperative behaviour due to inherent selfishness. So, while the Prisoner's Dilemma is often seen as a metaphor for the inevitability of betrayal and defection, the experiment of Flood and Dresher offers a different perspective. It shows us that when faced with repeated interactions, we humans are more likely to foster cooperation, build trust, and create mutual benefits. Rationally.