Prisoner’s Dilemmas and White-Collar Prisoners, Part 2

Despite its compellingness, there seemed to be something wrong with the Prisoner’s Dilemma (PD) game as a tool for predicting the behavior of real people. In the real world, co-operativeness is far more common than the initial models predicted.

It’s possible to account for this mismatch by positing a “social instinct,” which people follow despite the cost of them doing so. If this explanation were accurate, then there can be no accounting for the costs of co-operation under the prisoner’s dilemma, nor economizing for it. People just act co-operatively without regard to cost, so economics can have nothing to say beyond noting what the costs are.

Recently, though, another explanation has arisen from the studies of the game itself, though analyzing what is called the “iterated prisoner’s dilemma,” where the PD game is played multiple times against the same opponent(s). What makes this variant of the game different from the one-shot variety is the possibility for a co-operator to seek revenge against someone who defected against him/her earlier. Numerous studies have shown that, when payback is allowed for in this way, the optimal strategy more closely resembles everyday life.

According to the Wikipedia article on the subject, game theorist Robert Axelrod has identified four criteria for an optimal strategy in an iterated prisoner’s dilemma game: niceness, or initially giving a stranger the benefit of the doubt; retaliation, or making sure a defection is paid back in kind the next time ‘round; forgiveness, or the refusal to hold grudges once the payback has been administered; and, non-enviousness, or playing by the three rules mentioned above without letting someone else’s temporarily better score impel a quick defection.

These four criteria roughly square off with a lot of maxims from everyday life. “Don’t be rude.” “Don’t be a sap.” “Don’t live in your pain.” “Envy eats itself if it has nothing else to chew on.” Etc.

One of the interesting optimizations of the basic strategy that works the best – “nice” tit-for-tat – is the introduction of random unrated forgivenesses every now and then. If there’s a 1 to 5% chance of letting a defector off the hook, the average overall score of the player who does so will improve slightly. The improvement margin is greater if each player has imperfect memory of the other player’s, or players’, moves.

This modification makes for an interesting speculation, as it does approach somewhat the Pareto-optimal solution of co-operating always: what would the effect be of introducing a player who always co-operates, regardless of losses, into a bunch of tit-for-tatters who are already in payback mode due to someone defecting earlier? If the others have perfect memory for each opponent, then such iron co-operativeness would be met with corresponding co-operativeness, from every other player, to the perfect co-operator. In a simulation, it would be the perfect winning strategy; in the real world, it would encourage co-operativeness to the point where defection becomes a winning option again.

If the game players use tit-for tat with perfect memory of what they suffered earlier, but with no memory of the previous opponent in a multi-player scenario, then a universal co-operator will tend to go deeply in the hole, relative to everyone else, at first. He or she will be the person who will be burdened with other people taking out their previous hurt on him/her without passing it along to anyone else. Such a person will act as a “payback sink.”

The result of such a strategy, though, will be to increase the amount of co-operativeness considerably, but not to the immediate benefit of the universal co-operator. The result of such an increase will be a move closer to Pareto optimality for the entire group, where no improvement in one person's condition is possible whout making someone else worse off.

Regardless, though, Dr. Axelrod’s four criteria do closely approximate everyday business conduct. The business world could be seen as a whole series of multi-player Prisoner’s Dilemma games already in progress.

It’s important to remember, though, that game theory is value-free. “Co-operativeness” can translate into “I’ll give you a break on the remittances if you put my product on the middle shelf” – or it can translate into “I’ll go to my board and say that a 20% pay raise will bring my salary in line with a comparable norm if you do so too,” or “I’ll hire your son if you hire mine.” Even an iron co-operator may be so only with respect to a certain group, refraining to do so for outsiders - perhaps by avoiding them.

A lot of white-collar crime does have this co-operative, or collusive, aspect to it. That’s why prosecutions in this area have the effect of ripping apart established iterated PD-type games and replacing them with the one-shot original.