Relatively Prime is a new maths podcast from Samuel Hansen. I'm delighted that an early episode, The Toolbox, begins by discussing my favourite area of mathematics, game theory (the subject of my very first post in this blog). Samuel interviews the eminent writer on game theory, Steven J. Brams, whose book The Presidential Election Game I devoured when it first came out many years ago. Brams argues that Shakespeare had an intuitive understanding of game theory and discusses applications of the mathematics in Hamlet and Macbeth.
It is particularly fitting that game theory features in Relatively Prime because game theory contributed to the podcast's very existence. Samuel raised the funding for Relatively Prime through Kickstarter, a crowd-sourcing scheme. Various individuals pledged funds to make the project happen. If Samuel reached his target funding before the deadline, these pledges would be called in; otherwise they would lapse.
I was keen that Relatively Prime should be funded. I admired Samuel's previous work. With Peter Rowlett, he is responsible for the excellent weekly Math/Maths Podcast which has, amazingly, now been going for over two years. (In the interests of transparency I should note that I have contributed to this podcast on a couple of occasions.) Even though Samuel is responsible for the incorrect abbreviation for "Mathematics" in the title of that podcast, I was prepared to consider making a small financial contribution to make Relatively Prime happen.
So consider my situation last summer. I was willing to contribute (a little) to the project, but wasn't sure my contribution would be necessary. From my perspective, the ideal outcome would be that Samuel raised enough from other well-wishers, and I could enjoy the result without paying a penny. But I would rather make a contribution than see the project fail.
No doubt many others are in the same position. We can see how much has been pledged, and if five minutes before the deadline the project had been 5 dollars short, I would certainly have jumped in. But if the project (which sought $8000) were $5000 short just before the deadline, then it's not worth my while wasting time pledging to a lost cause. How do potential donors play it?
Well, I did what no doubt many others did - wait for some time to see what was happening. With a few days to go , there were enough backers to show that there was some interest, but as the deadline day dawned the project was a long way short, but word of mouth was building up. The last few hours were remarkably tense as the pledges started coming in, and suddenly the momentum built up and Samuel reached his target. I was one of the many who contributed on the last day. About 140 people, I think, contributed to Relatively Prime.
As a potential backer one uses game theory here to help achieve the desired outcome, which is that the project gets funded but one doesn't pay more than one's fair share when others were also willing to contribute. How does it work? Nothing significant is going to happen until fairly close to the deadline. I think the intuitive game theorist (like Shakespeare, apparently) would fix a maximum contribution they were prepared to make. They would make a very small contribution at a relatively early stage, to encourage other potential backers by showing that there is some interest, and would then wait until a few hours before the deadline, perhaps committing a little more early on the final day but then hoping that others' contributions will come in. At the last minute, if necessary, they would be prepared to go up to their limit if the target hasn't been reached, but they wouldn't throw all their money in early because that way other intending funders might be let off the hook.
Of course this game theory meant that if Samuel were to reach his target, it would happen at the very last minute (as indeed happened on 3 August last year). The cost of all this game theory was a very nervous few days for Samuel when he was convinced his project would fail. So it is entirely appropriate that Relatively Prime has opened with an illuminating discussion of this fascinating branch of mathematics.