A while ago, I made up this thought experiment
Imagine that you are playing this game:
You and 9 other players are asked to vote "200" or "300" by secret ballot. When all 10 of you have voted, everyone who chose "200" gets an equal share of £200, and everyone who voted "300" gets an equal share of £300. Your goal is to maximise the amount of money you get. Imagine there is no way of working together with other players, or finding out how they have voted. All you can do is to guess what they will do.
The dilemma is of course whether to go for the larger 300 prize, or whether to assume that this is what most players will do, thereby making the 200 prize a better option. That reasoning can be regressed infinitely...
I set up this web page to enable people actually to play the game, and I wondered whether anyone here would be interested in giving it a go? You can play the game by clicking this link and filling out the 1-question survey (optionally also saying why you made the choice you did).
(Just to be clear, nobody playing this game is really going to get any prizes. This is only an exercise in finding out what people would do. Thanks for you help with the experiment!)
BTW - is there a formal game theory approach to determining the optimal strategy? I'd be interested to know, but please be aware that I studied maths to 17 years of age and that was a long time ago. So I'm unlikely to follow a high-level explanation, unfortunately!
It sounds like a prisoners dilemma type of question - no 'correct' answer. If acting purely in self interest you should choose 300.
Further - you have no way of knowing how many iterations the average person will make. But you could assume that the probability of x iterations decreases as x increases.
So the 1st iteration is that everyone would pick 300 as it is bigger.
The 2nd iteration is that 200 is a better bet if 6 or more people pick 300.
The 3rd iteration is that 300 is a better bet if 5 people get to iteration 2.
The extra size of the kitty for voting 300 makes it the better choice in a large enough sample I think