On a relatively basic level, game theory can be used to explain a lot of seemingly irrational behavior. For instance, why do firms advertise? Advertising is very expensive. Wouldn’t two large, well-established firms in a market be better off not doing it? This would allow the two firms to increase their profits and they wouldn’t lose customers because their competitor isn’t advertising to try and take them away. Coke and Pepsi, Budweiser and Miller, DC and Marvel, advertising for these firms is not only a money-loser, it is also a peculiarity. Why do they do it? A seemingly unrelated question is why do so many professional cyclists and track sprinters take drugs? They have to know the side-effects by now. There are risks of being discredited as a fraud (right, Lance Armstrong?) and all kinds of health issues (right, all you studio wrestlers?). Yet they do it with impunity, paying significant sums to keep their behavior under wraps.
Of all the games in the game theory world, perhaps the most classic is called the prisoner’s dilemma. The name insinuates that the actions of bad guys might pose a predicament once they are apprehended. That is true but the quandary doesn’t just apply to criminals. It is this dilemma that explains why firms advertise and athletes cheat, and will finally help us answer the question of why heroes fight each other. Before we get to that answer though, we need to set up the rules of the game.
Please Read All the Rules Before Playing
All games have parts and game theory is no different. To begin, you must have players. An interesting game will have at least two players trying to use their mental prowess to best each other. The players also need to have a couple of options for how they are going to go about winning the game. These are called the strategies. What course of action will you take as the game progresses? Here is where game theory diverts from other types of economic analysis. The outcome of the game depends not just upon what strategy you adopt, but also on that of the other player or players. You need to incorporate the plans of the players you are up against into your strategy because your success depends upon not only your choices, but also the choices of your competitors. In other words, your actions are interdependent.
You also need a set of rules so that the game is played fairly. To understand the rules, it is important to realize that there are lots of different games that can be played and, as a result, not all games are the same. In fact, the rules will often dictate the outcome of a game and a little tweak to those rules results in a different predicted outcome entirely. There are a few things that must be firmly established prior to the playing of a game. One of those is to know whether you are playing a one-shot game or a game that has multiple, or perhaps infinite, stages. A one-shot game, as the name implies, occurs only once. As a result, you do not have an opportunity to respond to the actions of another player. This would be like playing a single game of rock-paper-scissors to determine who gets the last piece of cake. It’s a one-time, winner-take-all, type of game, and what strategy you adopt is based on what you know of your competitor. A game that is played multiple times allows you to react to what has happened in the past. If cake goes to the player who wins the best three out of five times the game is played, then there is an opportunity to react to the prior strategy of your competitor. So, if you are playing against someone who throws rock twice in a row, you might see a pattern and try to exploit it.8 If the game was only played once and you had no information about your opponent, you would essentially be playing the game blind.
A second rule that needs to be established is whether the game is to be played simultaneously or sequentially. This rule deals with when you make your move. Do both players go at the same time, or does one player go first and the other react to them? In a game of rock-paper-scissors the game must be played simultaneously. Both players must throw at the same time, otherwise it isn’t much of a game. If I could wait to decide what to do until after you had revealed your strategy, I would win every time and you would find the game pointless. Many games allow the participants to react to what their competitors do. If we are playing poker and you bid, I can call, raise, or fold. Because I have the opportunity to react to what you have done, the game is sequential.
These basic rules are enough for the game we will examine in this chapter because our focus is on trying to explain why heroes fight each other, that seemingly unnatural result of good guys failing to talk things out. Before applying game theory to comics though, there is one other important detail to consider. When the outcome of a contest depends in part on the behavior of others, it would make sense to gather as much information about the strategies of your opponents as possible. Sports teams do this all the time by studying film. Of course, teams know that their opponents are also watching past events so they need to switch up strategies every so often to keep their rivals on their toes. As research suggests, in some sporting events, randomization is the best approach for success.9 This means that you try to vary your strategies to prevent your opponent from determining a pattern in your actions that they could exploit.
This could be true of the comic universe as well. The players are the professionals of the crime-fighting and criminal worlds and they repeatedly engage with each other. As a result, both sides have data on the others’ reactions to particular situations. If you want to avoid always being caught by the hero, the criminal needs to vary their approach. Early in the graphic novel The Killing Joke, Batman admits to his butler-cum-confidant, Alfred, that “I’ve been trying to figure out what he intends to do. It’s almost impossible. I don’t know him, Alfred. All these years and I don’t know who he is any more than he knows who I am” (Moore, Bolland, and Higgins, 1988, p.17). Batman's inability to predict the Joker’s next move is the perfect example of the randomness that can affect outcomes in comics. Batman wants to apprehend the Joker, but determining Joker’s strategy is impossible due to the arbitrary nature of his actions. Joker will engage in some kind of crazy connivance, but what will it be? When the Joker is at work there is no way to tell.
He’d Never Rat Me Out … Would He?
Late one night the fine men in blue of the Central City Police Department drag two staggering, bewildered hooligans into the precinct. The disheveled pair are thrown into separate holding cells to await processing and, perhaps, a visit from a public defender. Before that can happen though, the cops want to get some information out of the alleged perpetrators. In one cell the stoic figure of Leonard Snart sits peacefully. He’s been here before and knows the routine. Snart has a list of aliases, but to most people he is known as Captain Cold.
Snart has been picked up for a relatively petty offense, especially considering his rap sheet. He was arrested for vandalism. Nevertheless, Snart has kept his nose clean over the past few years and appears to be on the straight and narrow, eschewing his former life of crime. Still, around Central City, fake bills have been appearing. A counterfeiting ring is afoot and the quality of the bills makes them nearly indistinguishable from the real thing. There is no evidence and there are no suspects, but word around town is that Snart is off the wagon. While he waits for what he expects to be the normal line of questions, Snart isn’t worried about the outcome. He knows the other guy and there is no way he’ll talk, even if Snart was part of the counterfeiting ring (maybe he is, and maybe he isn’t, he’ll never tell), the other guy is his best buddy, at least as far as criminals have best buddies.
Without warning, the door opens and in walks a young woman in a tailored suit. She sits down across from Snart and lays a folder on the table between them. She begins to ask the normal questions but abruptly stops when she sees the look in Snart’s eyes. This isn’t getting her anywhere, so she decides to lay all her cards on the table.
“Look Snart,” she begins, “we’ve got you on the graffiti rap, and with your priors you’re going away for two years, minimum.”
No surprise, Snart thinks. He was expecting this.
“But, you better help us out with the counterfeiting stuff,” the woman continues.
Not likely, Snart says to h
imself. That’s a serious crime.
“If we find you guilty on that charge you’re looking at twenty years with no possibility of parole,” the detective informs him. She stands up and moves toward the door.
“Leaving already?” Snart snickers.
“Oh yes. You see, even if you don’t help us, your pal next door is ready to talk. We’ve made him a nice deal if he turns state’s evidence and he’s willing to take it. One year. He knows you’ll be gone for twenty so that’s enough time for him to make a new life for himself far away. We’d offer you that deal too, but it doesn’t seem like you’re interested. Maybe you’ll change your mind in a few minutes. I’ve got to go take a statement.”
Snart’s mouth drops open.
“He won’t talk,” he gapes. “Mick would never do that!”
But as the door closes, Snart’s confidence is more than a little shaken.
Out in the hall, the officer smiles. Turning to the next interrogation room, she takes a breath and, without knocking, walks boldly in. Sitting there is Mick Rory, alias Heat Wave. He and Snart have been thick as thieves, literally, for a long time. Both members of the criminal group the Rogues, a team of DC-based criminals who frequently match wits with the Flash, they have been suspiciously quiet for some time now.
“Look Rory,” she begins, “I’m not here to waste your time. We’ve got you on the graffiti rap, and with your priors you’re going away for a couple of years.”
No surprise, Rory thinks. He was expecting this.
“But, you better help us out with the counterfeiting stuff,” the woman continues.
Not likely, Rory says to himself. That’s a serious crime.
“If we find you guilty on that charge you’re looking at twenty years with no possibility of parole,” the detective informs him. She stands up and moves toward the door.
“Leaving already?” Rory snickers.
“Oh yes. You see, even if you don’t help us, your pal next door is ready to talk. We’ve made him a nice deal if he turns state’s evidence and he’s willing to take it. One year. He knows you’ll be gone for twenty so that’s enough time for him to make a new life for himself far away. We’d offer you that deal too, but it doesn’t seem like you’re interested. Maybe you’ll change your mind in a few minutes. I’ve got to go take a statement.”
Rory’s mouth drops open.
“He won’t talk,” he gapes. “Snart would never do that!”
But as the door closes, Rory’s confidence is more than a little shaken.
Out in the hall, the officer smiles.
This is the prisoner’s dilemma. If both criminals keep quiet they will both get two years. Despite the officer’s claims, she doesn’t have enough evidence to convict them of counterfeiting. By the way, Snart and Rory are in cahoots. They are indeed running the counterfeiting ring, so if either wants to provide evidence for the prosecution, they could do so. The deal that has been offered is only good if one of the crooks talks and the other does not. If they both confess, they both get ten years. So, can Rory trust Snart to keep his mouth shut? Can Snart trust Rory? The answer is, they probably can, but they’re thieves and as the saying goes, there is no honor among thieves, even friends like Rory and Snart. As a result, each criminal has a dominant strategy to confess, which results in an outcome that leaves them worse off than if they had kept quiet.
A dominant strategy is a choice a player would make no matter what the other player did. To see this more clearly, let’s look at how the prisoner’s dilemma game is illustrated in a game theory matrix like that of Figure 4.1. Each criminal is labeled along one edge of the matrix. In this case, Snart along the side and Rory at the top. There are only two strategies here: Confess or don’t confess. Each cell within the matrix provides the number of years for each player. Those are the payoffs. To limit confusion, Snart’s payoffs are underlined.
Figure 4.1. The Rogue’s Dilemma.
Notice a few things about this game. Because it is shown in a matrix, the game is considered to be simultaneous. Players make their choice of strategy at the same time. If Snart goes first then Rory can easily choose the best thing for him given Snart’s decision. The question of whether he should toe the criminal line is an easier one. Since neither knows what the other will do with certainty before they make their choice however, it leaves them in a bit of a quandary. Additionally, this is a one-shot game. You do not have a chance to alter your strategy once you find out what your co-conspirator has done.
To find the dominant strategy let’s examine the potential outcomes. If neither Snart nor Rory confess, that puts the hooligans in the southeast box where each goes to jail for two years. This box yields the smallest joint number of years in prison and that is good for them, but individually they could be better off. If Snart changes his mind and confesses while Rory stays silent, the outcome for the game moves to the northeast box where Snart receives the underlined value of one year in jail, while Rory’s term goes from two to twenty! Thus, for Snart, if Rory is going to keep quiet and not confess, he is better off confessing because one year in the slammer is less than two. If, however, Rory decides he will confess, and perhaps he has told this to Snart ahead of time, Snart needs to incorporate this into his strategy. If he doesn’t confess, the dastardly duo is in the southwest box. Here Snart gets twenty years while Rory only gets one. Snart would be better off turning informant and confessing because he would cut his sentence to ten years. Ten years is a lot of time in prison but it’s far less than twenty years. So if Rory confesses, the best thing for Snart to do, in order to keep his jail time low, would be to also confess. Therefore, no matter what Rory does, Snart is better off by confessing, so that is what he will do, and that is what makes confessing a dominant strategy.
Rory’s logic should follow similar reasoning. Again, starting in the southeast box where neither criminal confesses, Rory sees an opportunity. If Snart isn’t going to confess then he should. That would cut his penalty from two years to only one. Thus, if Snart is not going to confess, Rory would be best served, in terms of less jail time, to confess. On the other hand, if Snart tells Rory that he will snitch no matter what Rory does then it is in Rory’s self-interest to also confess. If Snart confesses and Rory does not, the scoundrels would be in the northeast box. There Snart serves a year, but Rory gets twenty. By likewise confessing, Rory gets ten years, again, not an insignificant amount of time, but far better than twenty years. So, no matter what Snart does, Rory is better off by confessing.
Not all games have dominant strategies but the prisoner’s dilemma does. That’s part of what makes it a dilemma. There is a path that the criminals can take that results in less jail time no matter what the other criminal does, but that path leads to more combined jail time than one of the alternatives. This puts the crooks in a real pickle. They end up with a joint sentence of twenty years, rather than the aggregated four they could have had, because the dominant strategy leads to this suboptimal outcome.
In real life there are ways to avoid the prisoner’s dilemma. If you’ve ever watched a mob movie you’ve probably seen such a tactic. The mob uses the threat of bodily harm to you or those you care about to keep potential witnesses in line. If you confess, someone will either whack you, whack your kids, or torture your grandmother and your pets. It’s a grizzly business, but it is actually an attempt to get out of the prisoner’s dilemma. In the comics, the prisoner’s dilemma is often gotten around by the plain fact that supervillains break out of jail with relative ease.
That’s the prisoner’s dilemma in the case of jail time; but we’re not here to talk about criminals. We’re supposed to explain why heroes engage in non-hero-like behavior. It just so happens that if we take the prisoner’s dilemma and apply it to hero on hero crime, we have our answer.
What Heroes and Prisoners Have in Common
The dilemma we have just reviewed between two criminals can be explained by a lack of trust, but that doesn’t preclude it from impacting heroes. Situatio
ns such as Batman v Superman or Marvel’s Civil War or Injustice: Gods Among Us all have climactic, unexpected, punishing fights where we readers hold our collective breath as we wonder how they will play out. Yet, underlying the tensions between groups of heroes who had recently been on the same side is the question “why?” The implications of the prisoner’s dilemma can provide insight into these cataclysmic battles among heroes, not to mention some of the more minor skirmishes that we discussed earlier in this chapter.
Since Batman v Superman: Dawn of Justice was such a bad movie, let’s instead focus our analysis on Marvel’s Civil War.10 The movie and the comic take slightly different approaches in setting up the conflict. I am going to follow the comic storyline as it strikes a more tragic tone, but either way, the impetus for the disagreement is that a hero escapade results in unacceptable collateral damage.
Why Superman Doesn't Take Over the World Page 10
