I also have mused over this game on-and-off for the last 40 years or so, ever since a girlfriend's employer used to run lotteries for the employees using the scheme. "Pick a famous novelist; we will sort the picks into alphabetical order (family name first), and award the prize to the first one on the list that only one person picked." The game smells strongly of the Prisoner's Dilemma. To address Bernie's questions at all, we need to know what we are seeking to optimize in the so-called "optimal strategy". It might be the case that for _any_ strategy, a defector can beat out a monoculture following that strategy. On Tue, Apr 14, 2020 at 12:46 PM Bernie Cosell <bernie@fantasyfarm.com> wrote:

A half century ago when I was doing TSD rallying many rallies had a kind of "participation prize". you got to pick a number and the person with the lowest *unique* number got the prize. It struck me back then as an interesting mathematical problem -- the optimal strategy for "N" players. I had one idea: which if N was small, one of us would simply become the team captain and be the only person to pick 1 and then split the prize. Clearly not an optimal strategy [since the non-captain players could collaborate to have one of them cancel the captain's 1 and then one of them would win with 2 -- and so on with everyone sorta cheating].

For no good reason I got to thinking about this again recently and I wonder: is there a game theory analysis of the optimal strategy for N players? I'm guessing it might be something like "everyone picks a random number from 1 to N" but I haven't a clue..

/Bernie\ Bernie Cosell bernie@fantasyfarm.com -- Too many people; too few sheep --

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