Essay On Game Theory

Game Theory
By Trevor Chow

Introduction
Game theory is a branch of mathematics, which uses mathematics and mathematical models to study strategy and decisions between logical decision-makers who need to make competing choices in a strategic game.

A strategic game is a term to describe a situation where several logical decision makers face different choices of action, whereby they may win or lose depending on their choice and other’s choices. These strategic games are often situations of uncertainty, as the decision makers do not know what choices the other decision makers choose to make.

There are many types of strategic games, for example
• Two-person zero-sum game: one’s gain will mean another’s loss (used for military strategy)
• Many-person

However, if one writes down a smaller number than the other, this smaller number will be taken as the true dollar value, and both travellers will receive that amount along with a bonus/malus: $2 extra will be paid to the traveller who wrote down the lower value and a $2 deduction will be taken from the person who wrote down the higher amount.

The question is: what should both travellers do to decide the value they should write down?

At first thought, it seems that both should write down $100, since that is the maximum possible. However, thinking twice, the optimal price to write down is actually $2. This is because:
1. A first picks $100, as to get the most.
2. But A then thinks that B, who also wants the most will also write $100. So A will write $99, because then A will get $101 ($99+$2) while B will only get $97 ($99-$2).
3. However, thinking about it again, B will also do the same as A to maximise profit. Therefore, A will lower the price.
4. This cycle continues until A and B both reach $2, which is the minimum amount.

This is another classic example that shows why often, following the rational and logical decision will end up with the worst result (except for the airline). However, in the real world, most people actually will pick choosing $100, as they either have