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.