http://www.fox.com/fod/player.htm?show=house

House MD is the 2nd most watched drama series on the Cornell campus according to Facebook.

What makes a story good? complex characterization, intriguing philosophical concepts, witty dialogues, and of course, complicated social interactions between the characters.

House MD is known for its screenwriting excellecy. The seemingly compliated and twisted psychological games of the characters can be, in fact, modeled by game theory.

House is the king of mind games (and sarcasms). in the most recent episode, House finds out that his best friend Dr. James Wilson is dating Amber (nicknamed “Cutthroat Bitch”), one of the interns he fired. House goes all out to figure out whether Amber is dating Wilson to get the fellowship she wanted or dating Wilson because she loves him. In order to keep the nosy House from interfering with their relationship, Wilson and Amber had to play a game of whether or not to tell House about their affair. Assuming House suspected nothing, their payoff would look like the following:

AMber

Not tell tell WILSON

5,4 4,6 tell

7,7 3,5 Not tell

With Wilson’s payoff on the left and Amber’s on the right.

Wilson’s payoff will be the lowest if only Amber tells House because House will investigate his relationship with a vengeance as well as label him as a lying friend. If only Both Amber and Wilson tell house, he will be slightly better off since he is at least honest. If only Wilson tells House, House will feel important and enjoy strategizing with Wilson, and therefore Wilson’s payoff will be the highest among the cases where House knows about the relationship. Similarly for Amber, her payoff will be lowest if only Wilson tells House because House will go all out to stalk her and try to prove that she is using Wilson as well as shower her with sarcasms. If only Amber tells House, she would not be as low because at least she is honest with house, and if both of them tell House, her payoff would be even higher because there is less mystery involved. The highest payoff for both Amber and Wilson, however, exists when both of them not tell house. If Wilson does not tell House, Amber’s dominant strategy would be to keep her mouth shut; similarly, if Amber does not tell, Wilson’s dominant strategy would also be not tell. Here we have a Nash Equilibrium that intuitively makes sense: if House does not know about their affair period, then they could have the most peaceful relationship.

Assuming that House does suspect them having an affair, their payoff would look slightly different:

Amber

Not tell tell

4,3 5,6 tell Wilson

2,2 3,5 Not tell

The payoffs for both are highest when they both tell, because this way House will have less of a mystery to investigate. Their joint as well as individual payoff will be the lowest when both do not tell because House will get extremely excited, play Sherlock Holmes, and drive everyone insane. This time the Nash equilibrium occurs at both of them telling House the truth.

However, notice that if both of them tell their payoffs will be 5,6 each because House will still be interrogating both of them (Wilson’s payoff would be slightly lower than Amber’s because he has to face House at work everyday). If they keep their relationship a secret and House never finds out, their payoffs would be 7,7 (arbitrary number. The point is it would be higher than 5, 6) since they get to enjoy a real relationship. The couple decided to take a chance. They decided to try to keep their relationship a secret and hoped that House would not find out.

But House did find out. There are no games played between House and Wilson because there is nothing else for House to find out. For Amber, however, the story is a bit different. House suspects that Amber is dating Wilson to somehow get her job back.

House therefore decides to offer her a fellowship position in exchange for her leaving Wilson alone. House’s decision-making could be explained by the following payoff matrices:

Assuming that Amber is dating Wilson because she loves him,

Amber

accept reject

10, 5 11,10 offer House

5,4 15,8 Not offer

Amber’s payoff would always be higher if she rejects the fellowship offer because if she accepts the offer she would have to leave her lover. Her payoff would be slightly higher if she rejects House’s offer as oppose to not accepting the offer when House doesn’t offer because she gets style points for killing House’s smugness. For House, if he offers and Amber rejects, then he will know that his best friend is happy and hopefully he will be happy for Wilson too. If he offers and Amber accepts the offer, his theory of Amber potentially using Wilson would be confirmed and he will at least feel some satisfaction. If he does not offer the offer and Amber wants to accept the offer, House’s payoff would be lowest because Amber will stay with Wilson and she for sure does not love Wilson. If House does not offer and amber rejects, House’s payoff would be highest because Amber will stay with Wilson, and House does not have to offer her a price and negotiate with her. The equilibrium occurs, in fact, at this cell, since if Amber loves Wilson she will reject the offer whether or not House offers the internship, and House will not offer her the position since this way his payoff is maximized.

Amber

accept reject

10, 5 0, 10 offer House

-1, 13 -2, 12 Not offer

Here the game is different if we assume that Amber is playing Wilson in order to get the job. Amber only has a positive payoff if House offers the position and she accepts it. If House does not offer the position and she wishes to accept, her payoff will be very low and House’s payoff becomes high because he saves Wilson and his theory gets proven true (which is more important to him than anything else). If Amber rejects her offer, she will get a negative payoff because she does not get the job, but her payoff will be slightly higher if House actually offers a position because this way she would at least gain a LITTLE bit of self-assurance. House’s payoff when Amber rejects and he offers is lower than when Amber rejects and he does not offer because in the second case he does not need to give up some of his pompousness by offering Amber a job.

The equilibrium occurs, thus, with Amber accepting and House not offering, since Amber will always accept and House’s payoff is always higher when he does not offer.

This creates a problem for House. House does not know whether Amber is playing Wilson or seriously in love with Wilson, so it would be very difficult for him to decide whether or not to offer Amber a position. There is also the possibility that Amber might accept the position even though she is in love with Wilson, take the job, and then secretly continue her relationship with Wilson.

Instead, being the clever man he is, House merely hints the possibility of offering Amber a position, and lets Amber be the person who states her position first. House does not know whether or not Amber likes Wilson, but he does know that Amber’s dominant strategy is accept if she does not love Wilson and her dominant strategy is reject if she does love Wilson.

Thankfully, Amber and Wilson have real feelings for each other.

Yet, this brings another problem. According to the theory of triadic closure, a network of three people could only have either one positive connection or three positive connections. In the House, Wilson, Amber network, there are positive connections between Wilson and Amber and also positive connections between House and Wilson. The connection between House and Amber at the moment is most definitely not positive since he calls her “Cut-throat bitch”. If triadic close theory holds true, House will either have to become friends with Amber, or sever his friendship with Wilson. House is known for not able to interact with humans so the possibility of him forming a friendship with Amber is highly difficult, but his relationship with Wilson is so strong that many viewers on fox.com feel that it even contains homosexual undertones. Either possibility seem completely likely, or unlikely. Perhaps a premise of triadic closure theory is that the participants have to behave rationally, which is clearly a quality that House desperately lacks.