Game Theory: Not just a good save?
Maths teacher Mr Andrew Hon began his lesson with the Year 10 Athenaeum by discussing a picture of England goalkeeper Jordan Pickford showing his water bottle with all the preferred strategies of the opposition penalty takers written on it. Knowing the probable action of the penalty taker he could respond accordingly. Did it work against Switzerland…well he didn’t save them all but enough to ensure an England victory. But what lay behind Pickford’s strategy, how might we tailor our game playing strategy dependent on the information we have both about the rules of the game and our opponent?
This was the theme of the rest of the presentation. Starting with rock paper scissors the students talked about optimum strategies and then these ideas were transferred back to penalty taking. Is there an optimum strategy? Mr Hon talked about the Nash equilibrium and concluded that in penalty taking there were “better options” and demonstrated this mathematically. Of course, these strategies may need to be deployed over a large number of penalties, but that does not invalidate them.
Thinking about moves and pay offs is of course not limited to penalty taking, but as Mr Cavendish pointed out, also to foreign policy.
