Opening bad-3-corrupt_lzma2.xz in an editor reveals it indeed has the string ####Hello####. I don't know enough about lzma compression streams to explain how this appears in the "compressed" version of the payload, but it does.
> I don't know enough about lzma compression streams to explain how this appears in the "compressed" version of the payload, but it does.
From what I've read, the payload isn't stored in the archive, but rather the test file itself is a sandwich of xz data and payload: There are 1024 bytes of xz archive, N bytes of payload, another 1024 of xz, etc.
Do you have a (safe web view) version of those files? I would like to see what they look like to a casual observer. Judging by the 'tr' assembly command I would expect the bad-3-corrupt_ligma2.xz to be somewhat recognizable as script.
Indeed the Nash equilibrium is not always what we would like to call "optimal", especially in games with more than two players.
As you notice, it is possible the Nash equilibrium strategy will be crushed if more than one agent chooses a different strategy (i.e. a situation where players are deviating from a strategy in a non-unilateral fashion). If Agent 1 and Agent 2 work collude beforehand they can completely crush Agent 3. The Nash equilibrium only says the agent will lose more if they change while the others use the follow the same strategy (i.e. a unilateral deviation).
In defense of the Nash equilibrium, there are some reasons we can sort of assume that the two players will pick a strategy which happen work together to beat us by a lot. For example, one of the two other players could just play the Nash strategy along with us, in which case we know the other player will not be able to exceed the equilibrium value. There is no way the player can pick a strategy all by themselves which is guaranteed to win more than the equilibrium value. For the other players to actually have a guaranteed higher probability of winning, they must coordinate playing their strategy with the other player and trust that the other player will keep their word. This is known as forming a coalition.
There are some other notions of equilibrium which take this into account and do not permit coalitions to change the value (see: strong Nash equilibrium), but it won't exist for many games (like this one).
A small note: If you allow randomized algorithms, this problem is actually known to be in P^PP^PP^PP which is well within PSPACE in some sense, but still a ridiculously bad bound.
Unfortunately, it's impossible to do true uniform random over set of rows without doing something like count() over the things you are sampling over. You are looking to select something with probability 1/n, where n is the number of rows, so you must somehow, possibly implicitly, compute n, which is the count. So you'll always end up with at least O(n) assuming you have no pregenerated structure before running the query.
