The Prisoner’s Dilemma in Zero Escape: Virtue’s Last Reward

So, I recently picked up the Vita version of “The Nonary Games”, which includes two games: Zero Escape: Nine Hours, Nine Persons, Nine Doors and Zero Escape: Virtue’s Last Reward. I’ll talk about the games themselves a bit next week, probably. But today I want to talk about part of Virtue’s Last Reward. Since the game isn’t that old, I’ll put discussion of it below the fold because it will contain spoilers.

So, aside from the main gameplay, the game inserts what is essentially a Prisoner’s Dilemma element into the game. After you and your partners gain certain keycards, you go into another room where you can get rewarded with points if you make the right choices. There is, however, only one choice to make: you have to decide whether to Ally or Betray the person that you went through the gameplay with (it’s more complicated than that, but that’s good enough for our purposes). If you both choose Ally, you both get 2 points. If one chooses Betray and the other chooses Ally, the one who Betrays gets 3 points and the one who Allies loses 2 points. If both choose Betray, each gets 0 points.

Now, one key element here is that this is an at least somewhat iterative Prisoner’s Dilemma — as you have multiple rounds — and you need nine points to escape completely, and if your points fall to 0 or below you die. There is no limit on how many people can escape, but the door will only open once, and only stay open for a short time. Anyone who has nine points when it is opened can escape, and anyone who doesn’t have nine points when it opens cannot escape, and so will be left behind or will be killed trying to sneak through.

A couple of the characters make a big argument for how the only rational move is to betray (admittedly, before it is known that this game will iterate until someone escapes). But putting all the rules into context, it clearly isn’t the rational move unless you are an evil person. Everyone starts with 3 points, and so let’s imagine that everyone always allies every round from the start. Everyone needs six points, and it will take three rounds to earn six points, and at that point everyone can leave together, as everyone would have nine points. On the other hand, if everyone betrays from the start, everyone will get no points and will just keep running the rooms over and over and over again, without being able to make any progress.

You can imagine, though, that if you can betray on your first round and on your second round with someone who allies, then you would pick up those nine points in two rounds, and get out earlier. Except that if you betray on the first round, everyone will know that, and won’t be likely to ally with you in the second round, meaning that in that round you won’t make any progress. And even if you did pull that off, you would have left at least one or two people without enough points to leave with you, which would leave them trapped there to likely die. Since more rounds are allowed, to leave then when there’s no explicit time pressure — the “host” says that you can play 2 billion rounds if you need to — would certainly demonstrate that you didn’t care one whit for anyone else.

This gets worse if you end up against someone who only has one point remaining (ie they were betrayed when they allied in the first round). Since they can’t afford to lose points, they are almost certain to have to betray you. If you betray them as well, you make no progress. If you ally with them, you lose what you gained in the first round (well, almost; you end up one point ahead). So the only way you can win here is to either ally with them and gain the two points for allying, which will be hard to do. And if you can do that, you might try to maximize your points again — and get to leave immediately — by then betraying them anyway. Which will result in their death. Even if we could excuse you trapping everyone behind to probably die, directly and deliberately causing their death isn’t excusable.

And, on top of all of that, unless you can convince that person to ally with you even when they know you betrayed someone in the first round, you won’t gain. Everyone who plays against you will betray you so they don’t lose points and risk death, and only trustworthy people will gain points as both ally with each other. So betraying will always lead to a never ending set of rounds where no one can gain enough points to leave … at least, not until most people learn to trust each other. And if you got ahead of someone with betrayal, they aren’t going to be too happy at giving you the points you need to escape before they have them as well, and so will definitely insist on dragging you back level before they are willing to ally with you again, since getting out first is the only reason to betray in the first place, if you’re thinking it all through.

The virtuous person, seeing the outcome, won’t betray and will take the consistent ally route because they can’t be responsible for the deaths of others. They will, however, betray anyone they think will escape before everyone else can because that would be being responsible for the deaths of, at least, the other people who get left behind. But what would someone who is primarily self-interested do?

This is a prime example of how Hobbes’ Social Contract and Rand’s Objectivism treat these purported issues of self-interest, morphing it into rational self-interest. The rationally self-interested individual will, like the virtuous person, see what the outcome of the betrayal strategy is. Even if they are willing to kill off other people to escape, they’d have to know that the others will not be willing to be left behind to die, and so will try to foil them getting enough points to escape, by betraying them whenever they have the chance. As I argued at one point in the comments on Adam Lee’s analysis of Atlas Shrugged, the rationally self-interested person in any of these Prisoner’s Dilemma/Tragedy of the Commons type of problems will see that they can benefit if they can betray and the others ally … but will also note that the exact same reasoning applies to the others as well, and that if everyone follows that reasoning things will work out very, very poorly. Thus, it’s not a rational move for them to betray, and they’d have to realize that if the other people are rational they will conclude that as well. Given the absolute certainty that their move will be found out and that later rounds or interactions will work against them at that point, they will all conclude that the most rational thing to do is ally for the three rounds so that everyone can escape … unless they find themselves in a situation where they have reasons that betraying will benefit them more while the other person will benefit more from allying.

Such a case would go like this. Imagine that through some strange machinations, you have one person who has seven points and the other person has six points. The other person only needs two more points, and so allying with the other person will let them get out (or guarantee that they can get out, if they aren’t a totally evil person). Thus, at a minimum, they only need to ally with someone else, and so are likely to be more inclined to co-operate if a good story can be told by an up-to-now trustworthy person. However, the person with six points cannot get the points needed to escape if they ally, but if they betray when the other person allies they will have enough to escape. Even if they aren’t willing to leave the others behind, they can easily insists on maintaining their ability to leave at that point by refusing to ally with anyone else. Yes, this would drag out the game — as only people who hadn’t yet reached the proper amount of points would ally with each other — but they could indeed still leave anytime they wanted if the game reached a stalemate.

In cases like these, the commenters at Adam Lee’s blog declared that things would fall apart and so Objectivism failed. Except that there are two ways to avoid that consequence. The first is the use of social pressure, where if they betray you won’t co-operate with them in the future, on this or on anything else. That’s not really a concern for the person in this situation, since they wouldn’t really need co-operation anymore to ensure that they can escape. The other way is to provide an incentive — either a reward or a punishment — for them to co-operate anyway. In short, you make it be in their best interest to co-operate even though at the base level analysis betraying works out better for them. In the real world, you can pay them some to put them over the top — as long as it doesn’t outweigh the benefits you get from them co-operating — or do something that costs them more than they’d gain by betraying. Here, again, there doesn’t seem to be much more the person could want other than escaping, and the only punishment would be to deprive them of that somehow, which would be difficult to pull off. But in the real world, there are lots of things like this you can do. If your neighbour, say, is making a mess because it costs you more than it costs them, you can always retaliate by, say, making noise and then bargaining away co-operating with them on when and how much noise you can make with how much of a mess they can make. In Galt’s Gulch, people asked why Galt didn’t shaft the others on the power or Midas Mulligan on the land, but this reflects that sort of flawed thinking. If Galt shafted them on the power, they’d shaft him on the food or whatever other amenities he needed from them. As long as it benefited him for them to co-operate with him, he had no reason to betray them, knowing that he would lose those benefits of co-operation the instant he tried.

The long and the short of it is that while the game — and many people — insist that betraying is the only “rational” option, most rationalistic philosophies will deny that it is rational at all, precisely because it results in a much worse outcome for all people in the long run, including yourself. Neither self-interested nor virtuous people should accept that betraying is the right move here, all things considered, and it probably explains a lot about why society is the way it is that so many people think the “rational” option is one that, in the long run, has such disastrously bad consequences.

Tags: Objectivism, philosophy of gaming