There was a popular game show in STAR PLUS titled "Khul Jha Sim Sim". The rules of the game were very simple. The host of the show offers the player a choice of three closed boxes. Two boxes are empty, but the third contains an expensive prize like a TV, Fridge, Microwave Oven etc. The player doesn't know which box has the prize, but the host does. The player first has to choose one of the boxes. Next, the game show host will pick an empty box that wasn't chosen, opens it, showing that it’s empty. Finally, the host gives the player an option to change boxes. The player can switch from the box that he picked to the other unopened box. Is there any advantage in switching boxes? What would you do?
Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions in an attempt to maximize their returns.
Game theory can be applied to our everyday life because we are not the only stakeholders in the actions that we 
perform. It's always better to have an understanding of what would happen if you choose to follow a certain decision that we make. How many of us really consider the pros and cons before making a decision? How does our action influence others in their decision? Bargaining in a shop is a game. Bargaining the fare with an auto-rickshaw driver involves game theory. The driver would accept your offer if he is made to believe that you would choose an another auto if the deal doesn't work out. But on a lonely night with not much of a traffic, your bargain might not work.
"Game theory at work : How to use Game theory to outthink and outmaneuver your competition" is an interesting book for starters on GT. The book has full of examples and discusses on the various outcomes of a game. If you are interested in Game theory, check out this book. Game theory is also an interesting topic to discuss with your friends.
OK. Let's get back to our original question. Would you switch the box?
Answer:
You should definitely change boxes. Let’s label the three boxes as A, B, and C and assume that you picked box
A. Obviously there is a 1/3 probability that the prize is in box A and a 2/3 probability that the prize is in either box
B or C. Either or both boxes B or C are empty. Thus, after you pick box A, it will always be possible for the host to
open either box B or C to reveal an empty box. Consequently, the host’s actions do not affect the probability of
the prize being in box A. Before the host opened one of the two other boxes, there was a 1/3 chance of the prize being in box A, and after he opened one of the other boxes, there is still a 1/3 chance of the prize being in box A.
Let’s say that the host opened box B and showed you that it was empty. Now, since there is a 1/3 chance that
box A has the prize, and a zero chance that box B has the prize, there must be a 2/3 chance that box C has the
prize. Consequently, you should switch to box C because it will double your chance of winning.
Did you choose the same answer? Did you apply the GT concept of was it a gut feeling?
Another Teaser question from the book:
Assume that three people secretly write down a dollar amount on a piece of paper. They must pick a
whole dollar amount between $0 and $100. The person who writes down the lowest number wins the
amount she wrote down. If there is a tie, the winners split the total. Thus if:
Person one writes down $53 and
Person two writes down $22 and
Person three writes down $30,
then person two wins $22. If person three had also written down $22 rather than $30, then persons two
and three would have each received $11 because they would have split the $22. Find the reasonable
outcome in this game when all players are rational.
Answer:
All three people choose $1. This is a game better played as team. Imagine that all three of them choose to write $100. That would be the best outcome since everyone would get $33.33. But if both your opponents write $100, it's better if you write down $99. You would win $99 and a it's a better deal than $33.33. No one would want this to happen because they wouldn't believe the other two. The natural outcome is to write $1 because that's the least. Everyone writes $1 and wins 33 cents each. They would have been better if all of them had choose to write a higher number. The logic of game theory, however, compels the players of this game to bid against each other and throw away almost all of the available money.
There are more games like The prisoner's dilemma, Nash Equilibrium, threats, promises, negotiations etc. The book is a good read on all these games.
Game theory in Movies:
There are lot of movies that involves GT. The few that I can think of are Ransom, Crimson Tide, Dr.Strangelove, Failsafe, Hunt for Red October etc. No wonder that most of the movies are related to the cold-war era, where lots of tactics, negotiations, threats & promises were involved.
Any other good GT movies that you can think of?