haha, I wonder who's analyzed that game formally. feels a bit like the 2/3 game with flipped signs (https://en.wikipedia.org/wiki/Guess_2/3_of_the_average). for real numbers, the unique Nash equilibrium is 0, for finite precision numbers (which we're effectively dealing with in reality), the set of Nash equilibria is a bit more interesting.
but of course, Nash equilibria don't always line up well with human behaviour. for the 2/3 game there's empirical work showing that the best strategy against inexperienced players is betting somewhere around 20 iirc. would be interesting if there are papers that would give a similar rule of thumb how much of a "premium" you should offer over the nearest sensible round number
but of course, Nash equilibria don't always line up well with human behaviour. for the 2/3 game there's empirical work showing that the best strategy against inexperienced players is betting somewhere around 20 iirc. would be interesting if there are papers that would give a similar rule of thumb how much of a "premium" you should offer over the nearest sensible round number