The Lover's Dilemma

I expect that many of you have never heard of the Prisoner's Dilemma. I will explain it briefly here, but if you want more information you can check out the Wikipedia page about it here. It is a simple yet subtle game from the field of Game Theory, which is the mathematical study of, you guessed it, games. It goes something like this:

The police have arrested two men for a crime, but do not have enough evidence to convict either one. The prisoners are held in two separate interrogation rooms, unable to communicate with their partner, and are both presented with a choice either to remain silent (to "cooperate") or to rat out their cohort (to "defect"). If both of them remain silent, they will both serve six months in prison on lesser charges that the police can convict them of. If one rats out the other, then the rat gets a walk and the other serves ten years in prison. If they both rat each other out, they both serve five years in prison.

In a one-shot situation, it is obviously better to rat out your partner. While I won't give a real proof, the logic goes something like this: if you don't rat out your partner, you could serve either six months or ten years. If you do rat out your partner, you serve either no time or five years. While five years is not as good as six months, it beats the hell out of ten years, and no time trumps them all. What is interesting is that the outcome that is best for both as a pair, i.e., both cooperate, is not the best possible outcome for an individual alone.

To put numbers with this, both players start out with no points. If both cooperate, both get three points. If both defect, both get one point. If one defects and once cooperates, the defector gets five points while the other gets none. The player with the most points is considered to be the winner. When looked at this way, it is clear that defecting always either ties or wins but never loses, whereas cooperating either ties or loses but never wins. So, where's this "dilemma"?

Where the dilemma comes in is when the game is infinitely iterated, or played over and over again for all eternity, and both players remember previous rounds. For the people thinking about this as numbers, the points are cumulative and the player with the most points after any round is "winning" at that point. The dilemma is the possibility of retribution. Simply stated, the question arises that if one player defects in any given round to hurt the other player, then will the other player defect later for vengeance?

The infinite part is important here. For instance, if two people knew that they were going to play ten rounds, then the logical choice in the tenth round for both is to defect because there is no chance of further retaliation. Similarly, in the ninth round, since they both know they will defect in the tenth, the logical choice is to defect in the ninth round, and so on all the way back to the first round. But when the game is played an infinite number of times that logic fails, as there will always be one more round in which one player could have vengeance on the other. Do, however, note that playing the game for an unknown number of rounds has the same effect.

Now, why all this inane mathematical blather? Well, first and foremost it is because I happen to like inane mathematical blather quite a bit, thank you. But also I saw an interesting situation in which this form naturally arises: the relationship between two lovers. Think of every meeting between the lovers, whether a romantic date, a chance meeting, or anything inbetween, as a round of the game. Either lover can choose to be with the other (to "cooperate"), or to blow the other off (to "defect"). Neither lover knows for a fact, but must assume that there will be another encounter, so the infinite logic must be applied. If individual happiness is used as the measuring stick against which all outcomes are measured, the values of all of the outcomes are the same.

If both lovers cooperate, they both receive the value of being with each other. I justify the fact that, while this is the highest value for both combined, this is not the highest individual value for a couple of reasons. First, we all know that there many meetings which are the of the mundane, daily variety, and there are inevitably ones where one is simply appeasing the other, detracting from its value. Second, while every person has their qualities admired by their lover, every person also has idiosyncrasies that are best known and found most irritating by their lover. This is not to say that there are not high value meetings, but to say that they are not always high value. There are other things that one would want to do if they did not have to consider the other. Hence relationships involve sacrifice.

If one lover defects, then the defecting lover gets to do what they want without regard for the other, which yields the greatest value in individual happiness. If they are willing to blow off their lover, they are clearly not concerned with hurting them and suffer no negative consequences from it. On the other hand, the cooperating lover is left high and dry, which yields no individual happiness. One could easily argue that the effect is actually negative to the cooperating lover, and they would be correct, but I'll keep it simple, like the above model, and just say it gives none.

I say that the defector suffers no negative consequences, but I should qualify that statement. The defector suffers no immediate negative consequences. Since there will always be another round, the possibility of retribution is always present. This can, of course, degrade into a vicious cycle, so one lover at some point must forgive and forget in order to break out of the cycle.

If both lovers defect, then they do get to do what they want, which gives the outcome some value, but that value for each is tainted and significantly reduced by the knowledge that the other decided to blow them off. Having done it themselves, both lovers obviously know the selfish lack of consideration involved in defecting, and therefore, similar to both cooperating, the value of this outcome is equal for both, but less than the value of cooperation.

Lastly, the game must at some point end since humans are finite beings. There is the one involuntary ending, which is when one lover dies. This is not meant as a negative ending: may people have played this game with their lovers for decades before being forced to end it. The more interesting ending is the voluntary one: the one where one lover decides that the spread is too great and either claims victory or admits defeat. This ending is interesting because both are consummated by the same act, that of one lover removing themselves from the game in an act of total defection, and because either lover's perception of whether it was victory or defeat is never directly admitted, at least to the other, as neither lover is generally willing to tip their hand and reveal their scorecard. One may argue that eventually the scorecard is shown in the aftermath of the relationship, but I argue that the aftermath, as well as any fight during the relationship, is better understood by brinkmanship, in which tipping some of one's cards is used, but never the whole hand. I won't get into all that, but you can look it up on Wikipedia as well. I'll leave it as an "exercise for the reader".

What is the point of this inane analogistic blather? Firstly, so I can find a use for my newly made up word "analogistic", but secondly, and more relevantly, it is to ask a few questions. I do not want to know your answers, but only for you to ask them of yourselves. Think about past and current lovers, and imagine future lovers. What do your scorecards say and what does that say about you? More importantly, what do you lovers' scorecards say, and what does that say about you? Most importantly, are you satisfied with those cards or have you been caught in the Lover's Dilemma?

Dear Facebook

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