The interesting game theory dynamics of the button.

This is the part of the "game" that troubles me. Any "value" we assign to any color of flair is temporary and arbitrary.

That's a property of "value", though. Value is something that we assign to things, so it's always temporary and arbitrary, although in a practical sense, you're absolutely right that the value of flair colors is far more temporary and arbitrary than the value of, say, copper, which is actually useful for things.

Since there are no communally agreed-upon stakes in the game, there is no value to any outcome beyond what the people in the sub say there is at any given moment. The context could change at any time, and likely will change dramatically if something happens once the timer runs out.

In a situation like this, the stakes essentially write themselves. The flairs have relative rarity. If you have something rare, that confers status (even if it's just a silly status that's confined to a single little corner of the internet that doesn't matter). The value of the flair here is an emergent property of how the subreddit is set up.

Since we don't know what the button does (beyond re-setting the timer) or what the timer is counting toward, any definition of flair value is incomplete at this point.

I admit that I didn't consider what would happen if something unexpected were to happen once the timer hits zero (my working assumption is that the game will be over), but I admit that there are a couple possibilities that could entirely devalue the existing flair (such as the game starting over, the timer being allowed to run into the negatives, flair being arbitrarily deleted, etc).

Honestly, I think deleting the subreddit once it gets down to zero would be a hilarious troll move on reddit's part, although I'd imagine a lot of people who take the button Very Seriously would completely flip their shit, so doing that would be kind of a bad PR move on Reddit's part.

/r/thebutton Thread Parent