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Game Theory and “The Biggest Loser”

March 3, 2010

Subtitle: Why Michael is a Stupid Traitor.

I caught “The Biggest Loser” on tv today.  Now I admit I haven’t watched the previous episodes and may be missing something, but I was struck by how much someone with even a minimal understanding of game theory could gain over the average contestant.

The event that led to this insight came about midway through the episode. Michael – One of the players on the game – had won some challenge and had been given the power to divide the contestants up into two teams and choose who their trainers were.  He could also choose who had immunity for the week, but that person would end up on the team that lost a player next.

Michael’s choice was to split apart the families that had come on the show together and pit them against each other, put the strongest competitors all on one side (the side he put himself on) and give immunity to one of the less threatening players while putting his wife on the strong team (since the weak team will almost certainly lose, he effectively split them up too.

In other words, he effectively screwed over every single person on the show in one way or another for his own short-term benefit.

Some of the other contestants were worried coming up to this because “he was a game player”.  In fact, this is exactly what a GOOD game player would avoid.

One of the foundations of current game theory is based on the illustration of the “Prisoner’s Dilemma”.  Wikipedia has as good a description as any:

In its classical form, the prisoner’s dilemma (“PD”) is presented as follows:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects from the other) for the prosecution against the other and the other remains silent (cooperates with the other), the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

If it is a single decision, the rational choice is to betray your buddy. However, if there is a series of events where retaliation is possible, current theory and practice both say that greedy approaches fail. Basically, if you start with betrayal, you predispose everyone else to betray you in return. For this reason, WINNING strategies start off nice. Wikipedia lists traits for winning strategies as well:

By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.

Nice
The most important condition is that the strategy must be “nice”, that is, it will not defect before its opponent does (this is sometimes referred to as an “optimistic” algorithm). Almost all of the top-scoring strategies were nice; therefore a purely selfish strategy will not “cheat” on its opponent, for purely utilitarian reasons first.
Retaliating
However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as “nasty” strategies will ruthlessly exploit such players.
Forgiving
Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.
Non-envious
The last quality is being non-envious, that is not striving to score more than the opponent (impossible for a ‘nice’ strategy, i.e., a ‘nice’ strategy can never score more than the opponent).

Going by these criteria for good strategies, every other player in the game is now best served by joining together against Michael until he repents or is forced out.  Now, it is possible he will suddenly have a change of heart or come to his senses, make reconciliation quickly, minimize the damage done and get back into the game.  However, he would have to make a HUGE gesture quickly to be effective because it won’t be long before either he is on the chopping block or the teams are reorganized again or done away with and he is facing the entire group alone.

At that point, of course, he’s done for.

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