Are you the Bluff Master?
Bluff master was an Indian television game show that first aired as Dirty Rotten Cheater on PAX in 2003. It was also aired in France, Italy, Japan, UK, Hungary, Spain and Vietnam with different names. The game show is interesting as it exposes the ability of the players to cheat, lie and deceive in order to win a large sum of money. Basically, the game begins with six contestants with one of them pre-designated as the Bluff Master. Nobody else, including the host knows the identity of the Bluff Master. The main advantage that a bluff master gets over the other contestants is that he has access to all the answers to the questions on the game show. Hence, it is his call to either be honest and not cheat or cheat and win a lot of money in each round.
There are a total of five rounds and each round begins with a survey question like, “What is the best possible way to propose to a boy/girl?” The contestants need to guess one among the top ten responses in order to receive money with the lowest ranked getting around $250 to the highest getting $2,500. A contestant receives no money for giving an answer that is not on one among the top ten responses. The bluff master has access to this entire top ten list and has to choose to either give a high dollar answer to build their own bank or a low-dollar answer in hope of bluffing the remaining contestants so that he can remain in the show. At the end of the round, each of the contestants secretly vote on who they think the bluff master is depending on the responses for the survey questions. The top two voted contestants are then given a chance to convince why they are not the bluff master indeed which is then followed by another round of voting. If the contestants have identified the bluff master, the player is eliminated from the game and the remaining contestants share the bluff master’s bank. A new bluff master is designated among the remaining contestants and the game continues. If the contestants managed to eliminate a player who was not the bluff master then the money earned then the money earned by the remaining contestants is halved and goes to the bank of the bluff master. The bluff master remains the same in the subsequent rounds as well until he is eliminated or revealed. In the case of arbitrary voting, where there is no clear top two eliminations the money of the contestants is halved which provides them an incentive to collaborate. The bluff master now gets a chance to secretly eliminate an honest player in the game through a button hidden inside his podium.
Throughout the show, the bluff master has to weigh in the risk and return for cheating while answering the question. Similarly the other contestants have to make a decision to collaborate or not. There are pay offs associated with every decision they make and it is interesting to see what wins at the very end: honesty or deceit. Players’ strategies teeter totter as one after other honest player gets eliminated. The dominant strategy at the beginning of the game for the players is not to eliminate the bluff master but the player who has the majority of accusations as the payoff associated with guessing wrong is not too big. However as the game progresses, the dominant strategy switches to eliminating the bluff master as the payoff for wrong guess is now costly (their amount would be halved and by this time they must have banked a lot of money) while the right guess would lead to a positive payoff. The way players make decisions also changes as the game progresses. Initially, they accuse the player who answered the high dollar value response or has shown a lot of inconsistencies to be the cheater in the game but in the later rounds they tend to pick the person who has been consistently making money by answering medium dollar value responses. While the players are busy trying to spot the bluff master in the game, the bluff master needs to keep all their strategies in mind and make sure he banks a lot of money and that he does not get eliminated. In each round he can decide to either cheat or not. Since he knows the payoffs if he cheats there is more incentive to making a calculated response by deceiving. He also needs to keep the ongoing discussions about how players are making their accusations in mind. If they continuously choose to eliminate the player who guesses the high dollar value response then it is his best response to not guess the high dollar value even though he would get a high pay off. If the players choose to eliminate the player who has been consistently giving the right answers or the answers in the top ten list then he needs to make sure that he shows some inconsistencies by taking zero pay off in one round at least.
There are many applications of this game in the real world where people try to cheat to win. For example, in markets traders can cheat by passing in imperfect information about stock trends, students cheat in exams so they can score higher on their tests, and players cheat in games so they have an advantage over the other teams. The classic question boils down to if cheating is a good strategy or not and it is rather a two sided argument. Recently, a professor at UCLA gamed a game theory in his class by letting his students cheat to find out that the outcome was actually better than if they had not since collaboration leads to better ideas for solving a problem. This is similar to how the bluff master can win more money by making calculated decisions if he looks at the answers. On the other hand, in sports like badminton where players have some penalty for losing in the first round which provides them incentive to cheat. It is observed that it is up to the team’s best interest to try not to cheat as they have a high chance of getting caught early on in the game if they choose to cheat. This analysis suggests that it is good to not cheat at the earlier rounds of the game since the pay off for getting caught is higher (getting eliminated) than for getting the correct answer (maximum of $2500 in first round). In this way the game show takes bluffing to a whole new level as the payoffs get bigger and bigger.
References:
A sample round of the game show: http://www.youtube.com/watch?v=2dxqaXk9imI
About the show: http://web.archive.org/web/20030627214228/http://www.paxtv.com/shows/cheaters/
Where losing is winning strategy: http://www.quantitativepeace.com/blog/2012/08/when-losing-is-the-winning-strategy-game-theory-badminton-and-the-2012-summer-olympics-.html
Gaming a game theory: http://blogs.kcrw.com/whichwayla/2013/04/cheating-to-learn-how-a-ucla-professor-gamed-a-game-theory-midterm
Image: http://img15.imageshack.us/img15/7908/vlcsnap42764.jpg
