Example of a Decision Tree

A simple example of using a decision tree to help us with decision-making.

A couple renting an apartment and is wondering whether they should sign a 1-year contract on the rent.  If they sign a contract, their rent is guaranteed not to increase during the 1-year period. If they don’t sign a contract, their rent will increase by about $20 after 6 months.

This seems like a simple decision.  But there is a drawback to signing the contract. If the couple decides to terminate the contract before the end of 1 year, they are liable to pay up to 25 weeks worth of rent to the landlord, unless the landlord is able to get someone else to rent the place earlier. 

The couple intends to buy their own home if the right opportunity comes, so there is a chance that they would need to terminate any contract they sign.

Supposing the initial rent is $900 per month, what is the couple’s best option?

Let us choose the simplest situation first.  Let’s assume there is zero chance that the couple will terminate the contract.  So the decision tree looks like this:

The tree says that the option to sign a lease contract will result in a total 1-year rent of $10,800 ($900 * 12 months), while not signing a lease contract will result in a total 1-year rent of $11,800 ($900 * 6 months + $900 * 1.2 * 6 months).

But what happens if the couple finds their dream house and moves out of the house after 8 months?