The Numbers Game: Putting Yourself In Other’s Shoes

Perspective is essential.

In life, in your work and in everything that you do. It’s also essential in game theory when attempting to reduce a game to it’s simplest form via a process known as iterative deletion of dominated strategies.

The lecture below gives a simple game that illustrates this idea:

During class you are given a sheet of paper on which you must write a number between 1 & 100. The average number of everyone in the class will be calculated. To ‘win’, the number you choose must be 2/3 of the class average.

This game forces you to consider other people’s perspective. In order to think logically you need to put yourself in other people’s shoes, imagining what they are likely to do, and then determining your own strategy in response to your assumptions about the other player(s). 

This is a great game to introduce to a class of any age, regardless of experience in game theory, game thinking or mathematics. It’s simple enough that everyone can play, develop their idea of a winning strategy and engage in discussion around ‘why’ and ‘what if.’ Game Theory requires students to put themselves in other’s shoes – a valuable skill in life.

The solution to this particular game can be found by an iterative process whereby you systematically delete dominated strategies by considering other player’s actions. However the solution is not as obvious as you may first think.

Watch the video for a detailed analysis of a ‘solution.’

For a detailed description of some ideas on Game Theory check out Brian Weatherson’s notes.