http://www.chicagomaroon.com/2004/3/12/a-treatise-on-dating-the-prisoners-dilemma

The above article explains an interesting comparison between the prisoner’s dilemma which we discussed in class and dating using game theory. Like the prisoner’s dilemma game, this explanation shows why deception is a dominant strategy.

In class we learned about the prisoner’s dilemma which is a situation where two prisoners are caught by the police, put in separate rooms, and asked to confess to their crime. There is not enough evidence to convict them of the robbery they are suspected for, so the police need them to confess. It is a game theory situation because the best strategy for one prisoner depends on which strategy the other prisoner chooses. There are two options: either confess or don’t confess. If one prisoner confesses, but the other doesn’t confess, the one who confessed will get off and the one who didn’t will go to jail. If both prisoners confess, then they both go to jail. If neither confesses then they get a lesser charge of resisting arrest. The game can be viewed with the following payoff matrix:

.

.

Based on this matrix, the most socially beneficial thing to do is for both prisoners not to confess. However, confessing actually turns out to be the dominant strategy. That is because no matter what the prisoner 2 does (confess or not confess) the best choice for prisoner 1 is to confess. So because confessing is a dominant strategy they both end up choosing that, turn each other in, and both end up going to jail (-4) when if they had just held out they would only get a small charge each (-1).

In the article this dilemma is compared to the interaction between guys and girls who are interested in each other. According to the author there is an “incentive for all individuals involved to show disinterest toward each other, regardless of the reality”. The reason for this is that each person, while they might be interested, also desires to increase their perception of “exclusivity” by rejecting others. In this game “exclusivity works as a reward system because girls brag to each other about how many guys hit on them, and guys brag about how many girls they turned down. Similarly, girls communicate when they fail in attracting a guy, and guys do the same. In each situation, the players use communication to establish exclusivity, thus increasing their own desirability or communicating failure.” So in a social situation where a guy and girl are interacting, assuming both are actually interested, if both express this interest both get a relative gain because they will both have been successful in attracting the other sex. If both show disinterest then no one gains or loses, because no one was successful and no one was rejected. But if one person gets rejected by the other then the one who got rejected experiences a loss, while the one who rejected them will experience a gain in exclusivity. So even if both are interested there are positives of deception (rejecting the other person even though you are interested). The game can be viewed in the following payoff matrix:

.

.

Here it can be seen in the payoff matrix how no matter what choice the other person makes [lie (reject) or truth (don’t reject)] the dominant strategy for the other person is to lie and reject. That is because in this situation, like the prisoner’s dilemma you don’t know what the other person is going to do. It is socially optimal for both people to tell the truth, but because it is a dominant strategy to reject usually someone does. This is because “there are risks only when either player makes the decision to interact truthfully”. If a player chooses deception then there is no possible negative outcome, just a positive or a neutral.

So what is the author’s solution to this “dating dilemma”? He claims: “The answer is simple: do nothing! I call this tactic “pre-emptive protection of exclusivity.” Personally, I use my predictive abilities and realize that I’ll likely be shot down. And that she’ll probably brag to her friends about how “the columnist” tried to hit on her. So I do nothing. This is my way of really sticking it to girls whom I think aren’t interested in me.”

So there you have it, game theory explains why dating is so hard. When lying is a dominant strategy in male-female interactions it’s a surprise relationships ever work out.