Player each submit a number. Any format is permissable provided it can be read and understood by the organisers and a representative* selection of the players and that it unambigououlsey reffers to one and only one real number.

The numbers are inspected and the largest number wins.

The winner receives
all the entrance fee minus a reasonable* deduction for the organisers of the game

The entrance fee is calculated by some method, for example, flat rate, or logarithm of the submitted number, etc.

// matching of price to number size is part of the
game //

Ah, you buried the lede; entrance price being the
last thing you mentioned in your original post. As
matching the price to number size is part of it -
and you don’t know that size until the game is
closed - how do you set the price up front?

//how do you set the price up front?// By advertising it to potential players of course. You simply state the formula e.g. "entrance fee in £ is equal to the cube root of the number submitted (to the nearest £0.01)

I suppose the simplest game is just that the entrance fee is equal to the number submitted. Everything else is obfuscation.

//Ten to the power of the second-largest number entered// disqualified, recursive, not a stand-alone definition. Also you have to pay the entry fee based on the size of your submitted number, before the competition is run.