You Make the Play: Star Edition Take 2

So I got one great response to the problem. Unfortunately, I guess I should’ve clarified one part of the problem. When I make these posts about game theory, I’m working under the assumption that all else is equal, which is better known as ceteris paribus if you want to sound smart. In this case, you would assume that nothing else not specified in the problem description would remain constant. Ixidor and that Goblin Chieftain wouldn’t be doing anything this turn, and the game state would only change by the life totals.¬†Even so, Reynolds brought up some great points that I was looking to talk off of.

Reynolds mentioned that you can’t know for certain what Akroma will do after you. What we can do is try to figure out what our best move for every move that Akroma makes. Let’s assume Akroma attacks. Should we attack or not? If we don’t attack, we’ll be at 20 life. If we do attack, we’ll be at 15 life. So it seems like our better move if Akroma does attack is not to attack. Let’s assume, then, that Akroma doesn’t attack. If we don’t attack, we’ll be at 10 life. If we do attack, we’ll be at 5 life. So if Akroma doesn’t attack, we’re better off if we also don’t attack.

This seems like a reasonable way to think about this problem, at least in a very limited sense. There are very clearly some things that are wrong with this reasoning within a Magic sense beyond ceteris paribus. As Reynolds pointed out, there’s more to the game than just this one turn. We have to consider the game in a larger scope, so we’re actually repeating this situation over and over each time it’s our turn. Repeated games are a little trickier, so I’ll punt on that. Another point he brought up is that life isn’t the only factor here; even if we assume that all else remains constant, your choice clearly influences the opinions around the table, so it’s a little complicated. The biggest violation I made here to canon, though, is that Akroma will know what you chose to do when you make a choice. Fortunately, for the idea I’m trying to get across right here, it really doesn’t matter.

What this really is is a Magic setup for the classic problem, the prisoner’s dilemma. Here’s the description on wikipedia:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects from the other) for the prosecution against the other and the other remains silent (cooperates with the other), the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

Isn’t that grim? This is pretty famous. If you’ve played Baldur’s Gate 2, a genie in the beginning poses it to you. I remember in Dilbert that they split up a bunch of characters into rooms to try to get them to rat each other out for murder. Dilbert very heroically and indignantly points out that since every one of them is on the same side, everyone will shut up and that it won’t work, only to have the blinds pulled up and see that everyone else blames the murder on him.

Dilbert, in this case, is the sucker. It seems like a very attractive option to not betray anyone else; if everyone does that, everyone gets a lighter sentence. The bad news is that even if you convince everyone else to shut up, it’s still better for you to rat them out. Tattling (or not attacking Phage) is an example of a dominant strategy (real Game Theory term). A strategy dominates another strategy if it results in a better outcome for you regardless of how your opponents act. In this case of this Magic game, not attacking dominates attacking because whether Akroma attacks or not, your life total is still higher when you don’t attack than if you do attack.

Obviously, there’s a lot more going on in this situation. Potential take 3 here if you guys come up with more observations about this situation.

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