Prisoner's dilemma

The Prisoner’s Dilemma is omnipresent in modern media because it serves as a mathematical proof of social cynicism. It implies that cooperation is naive and cheating is rational. In turn, this implies an inevitable mediocre world where betrayal is the norm and cooperation is a hippy fairytale. At least, this is the lesson distilled in popular culture. However, this conclusion is mostly unfounded.

First, the Prisoner’s Dilemma is a simple game where only one turn passes. In multi-turn games, where agents interact many times, the best strategy is tit-for-tat [cite]. This has been heavily researched under many situations for many different game setups. Spiffy algorithms were developed to cheat, but still no general algorithm, however sophisticated, could beat tit-for-tat. This result was perhaps disappointing for the researchers, but it fits our intuition. So what can we conclude? Since the math of the Prisoner’s Dilemma holds for a single turn game, perhaps we need to set up society to avoid such games. This can be achieved by making decisions that account for an agent’s past actions. Hmm, no shit.

Second, the Prisoner’s Dilemma assumes perfect knowledge of the future while at the same time limiting communication. How do the prisoners know the outcomes of their actions? Indeed, can they even measure the value of the outcomes if they could forecast them? The real world is never so clean as the mind games. Maximizing value makes perfect sense in a game with clear rules and clear value functions and statistically understood futures.

Third, the prisoners are offered two choices, cooperate or defect. How realistic is that? What if they do neither? What if they try to escape? What if try to convert one of their captors? And yes, I am totally aware that this is a mental model, but a mental model that is unrelated to the real world tells us nothing of value.

Let me further illustrate this problem with an imagined dialogue between Alice (the professor) and Bob (the student).

Alice: Suppose you are a gang member. You and another gang member did a job together and the day afterwards were both arrested together at a local bar and sent to separate interrogation rooms. The cops explain that they know both of you are members of the gang. Based on membership alone,they can put you each away for 2 years. But they are not sure which of you performed this particular crime. If you will turn informer and rat on the other, then they will reduce your sentence to 1 year and sentence the other to 5 years. They will offer this same deal to the other prisoner.

Bob: Who is the other gang member? Do I know them? Is it someone who is honorable? Are they someone have seen be consistently loyal over the years, someone who would die for the gang?

Alice: Beyond this job, you know nothing about him.

Bob: This seems suspicious. We are pretty good at our job, how did they catch us. I’ve been in the gang a long time and haven’t been caught. Now, the first time I go out with this new member we get caught. I am suspicious that he is a plant. If so, asking me to rat on him may be a strategy to break me down so that they can force me to rat out others, such as my boss. But I certainly can’t do that. The boss knows where my family lives and the boss follows tit-for-tat to the tea.

Alice: The police assure you that the boss will never know.

Bob: How are they so sure? If they can see the future so clearly, why do they need us to inform at all? The calculation of costs is more complex than just number of years in prison. I might escape from prison. I might be let go early on good behavior. They might be lying about sentencing. I thought judges set the sentences. If I refuse to inform, I may be a hero in prison, so the 2 or 5 years in prison may be better than one year in prison as a known informer. Actually, doing a few years of hard-time is just what my resume needs.

Alice: Um, you may be overthinking this.

Bob: Oh, I’m just getting started. The value is hard to predict because the future is so uncertain and complex. But also, value itself is hard to define. If I refuse to comply, I will feel noble while in prison. What is the value of this feeling of nobility, how many months of reduced sentencing does it equal?

Alice: So what is your decision?

Bob: Assuming my partner is not a plant, then he may be loyal or not. I know I am loyal. That is hard requirement for the gang. I worked hard to build up my reputation. I assume he did as well. So both of us have made many cooperative choices in the past, so why not continue into the future? Why would either of us want to stain our reputations? Not a rhetorical question. If it is true that we can cheat without consequences, it would make sense to do so. There may not be consequences if 1) there is no way anyone will know we cheated (hard, since the police would know and my boss owns them) or 2) no future interaction will be affected by the betrayal. Perhaps we would move to a new circle afterwards that would not care about a betrayal of an out-group (the gang). Then we could rebuild a reputation.

Calculating the value of an action like this is a complex task with cascading uncertainty. We would need develop a model of value, a task perhaps no one has ever accomplished, and then sum values weighted by probabilities (which we cannot calculate) multiplied down deeply branching trees. In short, it is impossible to calculate the value of an action. So we use fast heuristics. A simple heuristic is to always act with integrity, be good to friends, make new friends when possible, and be terrifying to enemies. So, I would not rat out my partner. And they would not rat out me. You see, we are social creatures.

In conclusion, I believe moral principles are heuristics that are necessary specifically because we cannot estimate the costs of a specific action. The Prisoner’s Dilemma, like many moral thought experiments, is flawed because it ignores uncertainty. It is further flawed because it makes the untrue assumption that there is only one game and one set of players. This is never true.