Monday, July 22, 2013
"The Prisoner's Dilemma" is Tested and Comes Up Short
The basic version goes like this. Two criminals are arrested, but police can’t convict either on the primary charge, so they plan to sentence them to a year in jail on a lesser charge. Each of the prisoners, who can’t communicate with each other, are given the option of testifying against their partner. If they testify, and their partner remains silent, the partner gets 3 years and they go free. If they both testify, both get two. If both remain silent, they each get one.
In game theory, betraying your partner, or “defecting” is always the dominant strategy as it always has a slightly higher payoff in a simultaneous game. It’s what’s known as a “Nash Equilibrium,” after Nobel Prize winning mathematician and A Beautiful Mind subject John Nash.
In sequential games, where players know each other’s previous behaviour and have the opportunity to punish each other, defection is the dominant strategy as well.
However, on a Pareto basis, the best outcome for both players is mutual cooperation.
Yet no one’s ever actually run the experiment on real prisoners before, until two University of Hamburg economists tried it out in a recent study comparing the behaviour of inmates and students.
Surprisingly, for the classic version of the game, prisoners were far more cooperative than expected.
Menusch Khadjavi and Andreas Lange put the famous game to the test for the first time ever, putting a group of prisoners in Lower Saxony’s primary women’s prison, as well as students through both simultaneous and sequential versions of the game.
The payoffs obviously weren’t years off sentences, but euros for students, and the equivalent value in coffee or cigarettes for prisoners.
They expected, building off of game theory and behavioural economic research that show humans are more cooperative than the purely rational model that economists traditionally use, that there would be a fair amount of first-mover cooperation, even in the simultaneous simulation where there’s no way to react to the other player’s decisions.
And even in the sequential game, where you get a higher payoff for betraying a cooperative first mover, a fair amount will still reciprocate.
As for the difference between student and prisoner behaviour, you’d expect that a prison population might be more jaded and distrustful, and therefore more likely to defect.
The results went exactly the other way for the simultaneous game, only 37% of students cooperate. Inmates cooperated 56% of the time.
On a pair basis, only 13% of student pairs managed to get the best mutual outcome and cooperate, whereas 30% of prisoners do.
In the sequential game, way more students (63%) cooperate, so the mutual cooperation rate skyrockets to 39%. For prisoners, it remains about the same.
What’s interesting is that the simultaneous game requires far more blind trust out from both parties, and you don’t have a chance to retaliate or make up for being betrayed later. Yet prisoners are still significantly more cooperative in that scenario.
Obviously the payoffs aren’t as serious as a year or three of your life, but the paper still demonstrates that prisoners aren’t necessarily as calculating, self-interested, and un-trusting as you might expect, and as behavioural economists have argued for years, as mathematically interesting as Nash equilibrium might be, they don’t line up with real behaviour all that well.