You are the weakest link, Goodbye!
The Weakest Link is a television game show that first aired in the United Kingdom in 2000 and since then has been adapted in different languages in at least 45 countries under the same format. It provides a good source for people’s strategic behavior and assessment of human decision making in a real life situation with large rewards at stake. The rules of the game are as follows-
1) There are 9 contestants at the start of each game who answer trivia questions one by one, thrown at them by the (particularly mean and strict taskmaster, mostly female) host. There are several time bound rounds, at the end of which one contestant gets eliminated after the contestants vote amongst themselves. The length of each round decreases by 10-15 seconds successively.
2) The aim of this game is to produce the longest chain of right answers, that is, the maximum number of right answers in a row. As the contestants keep answering questions correctly, their money keeps building up until a contestant says ‘Bank’ before his turn to answer and all the accumulated money gets stored in their collective account, after which the chain starts from 0 money again.
3) If a contestant gives a wrong answer, the money resets to 0 automatically and all the money that was collectively accumulated by the contestants prior to this contestant gets lost. Also, any money not banked before time for that round runs out is lost too.
So the basic idea is- a round starts, contestants answer questions as quickly as possible (to maximize the amount of money earned by answering most questions in a limited time), the contestants call out ‘bank’ periodically to save their earned money, the round ends, contestants vote and weed out the weakest link- the person who slowed them down or answered most questions incorrectly. At the end, two players remain who go against each other in a penalty shootout format of 5 questions. If that is indecisive, they go on to a sudden death. The winner takes home all the money gathered.
The most important point here is that the contestants have to weigh the risk/return factor- that is, is their strategy for maximizing their payoff also compatible with rational decision making? For example, it is imperative to call out ‘Bank’ at the right time. They risk losing the money if they don’t bank it but there are compensations, because the next question after each correct answer is worth more money. Banking after 3 questions yields more money than banking after 1 question, but it is difficult to form a 3 question consecutive correct chain when the questions are harder. The greed for more money may drive contestants to not bank, and this decision might lead to a lot of money loss in the event of a wrong answer. Banking frequently on the other hand doesn’t let any money build up in the account that could have if they had not banked and got the next answer correct. The dominant strategy (at least theoretically) for the strong teams is to bank after 6 consecutive right answers, only if the contestants have the nerve to wait that long. The dominant strategy for the weak teams, intuitively, is to bank after every question.
Moreover, unlike usual games, the game show ‘The Weakest Link’ is a game where the players’ strategies and strategic incentives switch as the game progresses. At the start of the game, eliminating the weakest links is the dominant strategy. This is understood since a player would love to keep the smartest people in the competition to accumulate the most amount of money if he should win in the end. As 4 or 3 contestants remain, the dominant strategy is now to eliminate the strongest player in order to up their own chances of winning. The value of building the prize pool becomes outweighed by the question of whether a contestant can beat another contestant in a head-to-head challenge. Ideally, one would like to be competing against a low-skilled opponent in the final round to increase one’s chance of winning the final prize.
This game is interesting in the sense that the dominant strategy for this game changes as the game progresses, and also changes depending on the strength of the group (smart versus not-so-smart). There also has to be a sufficient amount of interaction between the players in the earlier rounds to collaborate and make as much money as possible, until of course the final round when they play against each other.
http://www.newscientist.com/article/dn1800-strongest-strategy-for-the-weakest-link-revealed.html