John Von Neumann was a mathematician and one of his many accolades was applying mathematics and his observations of traditional games to create a new discipline – Game Theory. This involves a mathematical approach to decision making whereby different strategies can be assessed. It a tool that not only can be used in Economics, but also can be applied to a broad range of areas and fields of study.
Just as I arrived at work, I was listening to Radio 4 and heard the introduction to the programme In our Time. This one in particular caught my attention because of the name mentioned – Von Neumann, and after arriving in my office I then listened to the discussions surrounding game theory.
The main link is to the discussion from BBC Radio 4, led by Melvyn Bragg, with guests: Ian Stewart, a Professor of Mathematics from the University of Warwick; Andrew Colman, a Professor of Psychology at the University of Leicester and Richard Bradley, a Professor of Philosophy from the LSE. I’ll keep it brief and simply say enjoy!
- What is game theory? How is mathematics relevant here?
- The discussion talks about co-operative and non co-operative games. What is the difference between them?
- In the game – walking down the street – draw out the matrix and show whether a Nash equilibrium exists.
- Draw out the matrix for the game ‘Rock, Paper, Scissors’. How can game theory be applied to this game? What is the best strategy to win this game? Can there be a winner?
- Draw out the matrix for the problem of littering when it is non co-operative. Is there a Nash equilibrium?
- What is the Prisoner’s Dilemma? Give some examples of it. Explain why it is an example of a dominant strategy game.
- How is game theory relevant to broadcasting? Think about the role of auctions and also the information given in the Financial Times article.
- Explain how game theory is relevant to the Cold War.