Sunday, October 18, 2009

Movies: I want to play a game, Part 3 - Don't everybody all volunteer at once.

In this last post on what game theory can teach us about the Saw franchise, we're going to cover traps that involve three or more players. But before we do that, we should quickly recap posts one and two.

To start, the only factor you can know that effects the outcome of your game is the number of players, where "player" is defined as a person whose choices can affect the outcome of the game.

In a single-player game, you've always only got one option for survival: play the game.

In a game with two-players, your playing either a zero-sum game or a deadlock game. Either way, the only survival option is to play; but everybody in the trap needs to evaluate whether or not they are really players or not, or you could end up turning a deadlock game into a zero-sum game.

Most importantly, in any game with one or two players, your only chance for survival is to play along. Always choose to play.

On to group games!

Jigsaw model 1.0, John, was not a big fan of building traps with more than three players in them. Perhaps this was a purely logistic issue: As his cancer began to eat away at him, the idea of constructing and organizing taps involving multiple players was simply outside the his physical performance profile. It might also be an issue of access. Once Jigsaw 1.0 picked up disciples, we get two large games featuring eight (Saw III) and five (Saw V) players. Jigsaw, a former architect, focused on individual sins, mostly the kind he could discover through his time in the his wife's health clinic or his own time in the Doc Lawrence's hospital. After he picks up Hoffman, a police detective with access to people's criminal records, Jigsaw starts snatching up networked groups: All the victims, except one, in Saw III were criminals who were caught through evidence tampering by a single detective; all the victims in Saw V were linked to a dubious Atlantic Yards-style land-grab development scheme. Regardless of the reasons, there are only two mass games in the franchise as of this writing.

The first group game involves as set of eight people waking up in a house full of traps that is full of a slow-acting nerve agent. The group must negotiate a series of traps, one per member, in order to retrieve an antidote and escape the house. In the second game, a group of five people must progress through a series of chambers, each of which contains a Jigsaw style test. Plus, Dexter's wife is one of the players, which is funny because you half expect Dex to show up and save her.

The first thing that's different about games with three or more players is that, for each individual player, deciding not to play may be a viable survival option. Unlike single- and two-player games, playing along with Jigsaw may not always be the best option.

In Sawworld, games with three or more players best resembles a well studied game theory game called the volunteer dilemma. Basically, the game breaks down like this: To achieve a positive outcome N number of players have to choose, in Sawian terms, to play; but playing comes at a cost (from disfigurement to potential death) so, provided that N can equal less than the total number of players, the best strategy for each individual player is not play and hope that the other players will take up the slack needed to reach N. In normal people terms, it's the reason you most likely don't donate money to NPR. You know that you want public radio and that public radio requires donations from listeners, but you also know from experience that enough public radio listeners do kick in that they can continue broadcasting without your contribution. Consequently, you know that you can get what you want without making a sacrifice. Therefore, why make the sacrifice? Of course, the dilemma is that if everybody followed the same logic, nobody would donate, public radio would collapse, and nobody would benefit.

In Sawian terms, the more players in a game that choose to play, the less necessary each individual contribution is. This means that, in theory, if the game's conditions can be satisfied without sacrifices for every player, than your best option is opt out of playing the game and let other players play the game for everybody.

We should note here that "playing the game" has a very specific meaning in our context. When we say a player opts to play the game, we mean that the player chooses to play the game according to the rules and expectations Jigsaw has set for the game. Not playing the game does not mean that you are inactive. Rather it means that you are choosing not to go along with the plan as presented. Saw III has an excellent example of a active non-playing character. In that film Xavier, a gansta type, decides that he's opting out of the game. However, his form of opting out means that he forces other players to run through the traps, taking damage meant for him, moving the game along without any sacrifice on his part.

That's all good and well for Xavier, but it screws the rest of the folks in the game. This is known in economics as the free rider problem: The more you work for the common good, the more it benefits others to let you work for them. This can lead to a death spiral in which more and more folks depend on the work of select few. That's unsustainable and the collapse screws everybody.

(WARNING POLITICAL CONTENT: This is, for those who may have stumbled here on a game theory Google search, game theory is an unintentional, but brilliant critique of free market ideology. Games like the volunteer dilemma, the prisoners' dilemma, and the tragedy of the commons show how rational self-interest can lead to less than optimum results. Give it up, fanatics.)

So what's the solution? Here's where the Saw series is horror at its best. The solution is that, in a game with three or more players, you need to get really fucking Fascist. You need to practice enforcement ruthlessly. Think back to the mausoleum trap we discussed last post. The mausoleum game turned from a win-win deadlock game into a zero-sum "one of us is going to die" game the moment one of the players chose the non-optimum strategy. When faced with a player that was working against the winning strategy, the winning player enforced the optimum strategy. Fatally. That's what you need to do.

If you find yourself in a game with three or more players, you need take a serious moment of introspection. Ask yourself: "Am I an utterly badass motherfucker who could totally bend all the other players to my will with the threat of violence?"

If the answer is genuinely yes, then you can enforce your unilateral decision to not play. Your best strategy is not to play and, instead, to force the other players to play the game - sucking up the damage meant for you and winning for you.

I should note here that Xavier, the Saw III character who tries this strategy, is a cold-blooded gangbanging mo-fo with an absurdly gym-hard physique and no qualms about applying heavy manners to any situation. And he fails. He can't enforce his strategy. He acts as a the "you must be at least this gangster to ride this ride" sign on this strategy. If you think you're more sociopathic, hardassed, and amoral than Xavier, then rock this strategy. But be honest, you probably aren't.

Let's say that you're not an insane gangster, then your problem is how to eliminate the free rider problem. The more free riders there are, the more likely you are to to get mauled or die without actually reaping the benefit. To do this, you've got to make the consequences of not playing worse than the consequences of playing. I'm going to propose that your best strategy is to organize with any other players who agree to play and enforce the " we play" strategy. Anybody who announces that they aren't going to play, gang up and force them to play.

If you're clearly in the majority, I recommend establishing a policy that the "yes" players announce that they will immediately kill any player chooses not to play. This eliminates the free rider problem by making playing, with its chance you may survive, better than the certain death that will come from not playing.

If you're in the minority, then go on strike. As stupid as is sounds, just sit down and refuse to anything. In a Saw context, everybody loses if nobody plays, but there's a chance everybody might win if somebody plays. You need to make sure nobody plays so long as anybody chooses not to play. This will also eliminate the free rider problem.

Admittedly, all these strategies are pretty foul as you basically start threatening the dudes you're trapped with. But, dude, you're in a deathtrap. Get tough.

Thanks for sitting through this series, which was basically me geekin' out for three entries. But seriously though, next time you wake up chained in a death machine, good luck.


Anonymous said...

Great posts, even if there isn't a lot I can add.

two minor points though:

1. "To start, the only factor you can know that effects the outcome of your game is the number of players, where "player" is defined as a person whose choices can affect the outcome of the game."

Isn't "knowing why you've been chosen as a player" another important factor? And if it is, doesn't it also gives us valuable clues about the kind of game in general (zero sum or deadlock, should we expect that other persons will be players or not, etc.?)?

2. I don't want to derail the discussion here, but this paragraph:
"WARNING POLITICAL CONTENT: This is, for those who may have stumbled here on a game theory Google search, game theory is an unintentional, but brilliant critique of free market ideology. Games like the volunteer dilemma, the prisoners' dilemma, and the tragedy of the commons show how rational self-interest can lead to less than optimum results. Give it up, fanatics.)"
doesn't seem all that accurate to me either - as far as I remember applied game theory the volunteer dilemma and the tragedy of the commons are usually used to show why privatisation is superior to government involvement and thus an affirmation of the free market ideology, whereas the prisoners' dilemma doesn't really have a lot to do with the free market at all as it is almost exclusively a micro- economics concept.

CRwM said...


Two interesting points.

To the first point, I'd say it might make a difference, but not always. I say this because, more often than not, Jigsaw tells his victim why he's been selected right away. Take, for example, the dude covered in flammable jelly in the first film. He's told right away why he's in the trap, but that doesn't make the trap any easier to negotiate.

However, in some cases the reason somebody is selected and their "sin" are not exactly the same thing. For example, Detective Matthew's in Saw II has been selected because he frames crooks when he can't find real evidence. But his real problem is impatient rage. That's what he's really being tested for. If he understood that his temper was what would sink him, perhaps he could have checked it.

Furthermore, part of being a genuine player these games means being able to make a real choice about whether to play or not. In that sense, the more information you have about your situation, the better.

That said, it doesn't really change anything. The only winning strategy is still to play. Whether he could figure out that his rage was being tested or not, his only winning strategy is to play.

I would say knowing why your being tested, and what specifically about you is being tested, would add more reason to play, but that would just reinforce what we've already figured out.

To the second point, the tragedy of the commons and the volunteer problems can occur whenever we're talking about a shared resource, be it a government program or a limited resource being used by private industry. The tragedy of the commons can be used to show why public money pools get depleted fast, but it can also explain why private industry, pursuing its own rational self-interest, can end up destroying the resources it needs to exist.

For example, in the absence of externally applied limits, it makes sense for fishing companies to overfish. Not only does it amount to a short term gain, but other companies can be expected to do it as well - meaning holding back in favor of protecting fish stocks for the future is a fool's game. Fish the hell out of it now while there's still fish to get!

The point is that game theory shows us that rational self-interest does not guarantee optimization. Is it always the worst option? Certainly not. But will the invisible hand of the market - a metaphor for the cumulative action of masses of rationally self-interested agents - always guide us to the best answer? Not always.

As an aside, prisoner's dilemma applies to many macro-scale phenomenon - notably trust regulation law and international defense spending.

Though, as I said, I'm no expert. Mostly, I'm just remembering Prof. Ben Polak's Yale course on Game Theory (it's online - I'm not that edjumakated) and one of his Five First Lessons: "Rational decisions can lead to outcomes that suck."

Thank you for the well considered response. It's always a pleasure to get meaty comments.

Troy Z said...

If you haven't already, there are also several chapters, in particular the penultimate ones, that address the issues of rational self-interest in private business and public policy in Jared Diamond's "Collapse: How Societies Choose To Fail Or Succeed," and, more to the point, how the mechanics of when those instances of "Not Always" can be redirected into positive action.

CRwM said...

Mr. Z,

Thanks for the head's up. I'll check it out.

Madelon said...

I wanted to read through all three posts before commenting, so here goes...

First of all, I enjoyed reading and thinking about this. The approach you have chosen to look at the traps and underlying mechanics makes for a very interesting thought experiment. As far as the basic concepts of playing y/n and strategies for games for one or two players, I completely agree with the outcome. However, I am not so sure about the multiplayer approach that is discussed in the third post.

As you mentioned, both Saw III and V featured traps for three or more people, and (to quickly recap) your solution would be to either become a badass mo-fo who screws everyone over, or, if you're not that person, try and thwart the game by not doing anything. Basically, your answer is to toughen up and resort to hardcore individualism and selfpreservation at the expense of others (feel free to correct me if I misread). Unfortunately, it seems that this strategy would not lead to a successful outcome of a multiplayer game (at least not the games as they are set up in Saw III and V).

Allow me to explain. As you already pointed out, things don't really work out too well for the badass mo-fo of III, Xavier. Secondly, because of the deadly nerve-agent that is working on all participants, stalling the game for too long would lead to certain death. The people involved in the game as laid out in III are forced to act (and thus to play). This situation, then, would have to result in an 'eat or be eaten' approach (as you suggested), at the expense of the weaker players. The point being: the proposed defense strategy, based on not taking action, is immediately out the window.

As for Saw V, although two of the five players eventually make it out (more or less) alive, the 'eat or be eaten' approach didn't work here, either. As Brit and Malick discover in the last room, the game was designed for five people to make it through to the end, cooperation being key. Although the badass approach would have some merit (by effectively turning the 'blood donation' trap into a zero sum game), it would have been possible for all players to get out alive.

If we focus purely on selfpreservation, then the 'survival of the fittest' strategy might be helpful. However, it seems that there might be other factors to consider (cooperation, possible plotting and backstabbing (again: consider Malick in Saw V)) when the number of players grows that can throw a spanner in the works and add to the factors that define the outcome.

CRwM said...


Good points all. Larger multiplayer games are tricky.

I should clarify my points. You're right that, in some cases, these strategies lead to the survival of some when, if played differently, the games could have come out better for more of the players. I'll admit that's true. It's a product of the assumption at the beginning of the series where I said that, for the purposes of this thought experiment, we'd assume that individual survival was the goal of each player. We'd have to rethink the multiplayer game strategy if we changed that assumption.

On going solo in a multiplayer game: My position is that it will only work if you can, in fact, enforce your will on all the other players. And that, as I said, is pretty unlikely. For most people in most traps, going solo is not a winning strategy.

I see your point about using inaction to get rid of free-riders, but I disagree in that case. The nerve agent is what actually makes inaction such a powerful strategy in that situation. Through inaction, or the threat of it, you make sure that free-riding is a losing strategy. There's nothing to ride. I should point out that inaction should only occur when you've got a free-rider; the idea isn't to just sit through the whole game, but to "strike" only when somebody ceases to work with the team as a whole. When they start working with the team again, you quit striking and move on.

As a final thing to consider, in Saw 5, under the terms of the thought experiment, the number of players for the blood extractor trap is only two. Remember that I posited that every time a game factor changes, including number of players, the players should consider themselves in a new game. In S5, once the game dropped to two players, the winning strategy was to play every game no matter what your partner chose to do.

Still, interesting points. Maybe the better claim is, when you're in a large multiplayer game, decide if you're going solo or team. If solo, you need to be able to provide real enforcement of your decision. If team, you need to develop a free-rider elimination strategy. What the enforcement and elimination strategies may be are determined by the conditions of the trap and the decisions of the other players.

OCKerouac said...

I am fascinated and angered by this post series. Fascinated by the thought provocation that can come from the Saw franchise, and equally angered that I now feel compelled to actually watch some of these films again... Good work as always.

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