This post will look at The Hunger Games as a source of inspiration. As such, there will be spoilers. You have been warned.
If you haven’t read the book and don’t intend to, Wikipedia has a decent synopsis. For what it’s worth, I found it to be an enjoyable read, but you can pretty safely avoid the other two books in the series. It’s dystopian sci-fi, but it has relevance to running a D&D game. While the book borders on sci-fi and might be classified as action-adventure (it’s technically listed as young adult), it is still applicable to a fantasy game.
It’s okay for the world to suck, including the government.
In the book, there was a rebellion and the government punishes the descendents of the rebels in a variety of ways, not the least of which is the actual hunger games. Prior to the lottery, much is made of the oppressive government and the dreary, impoverished existence forced upon the descendents of the rebels. Things are so bad that, just to feed her family, Katniss must risk her life and defy the law. After Katniss and Peeta become the Tributes and head to Capital, the focus shifts to the decadence and cruelty of the elites.
Obviously, the Dark Sun campaign setting shows that there’s a place for stories of hardship and survival. Beyond that, however, it’s okay for governments to treat their people badly. When I hear people talk about their games, nations are most often ruled by benevolent monarchies where the taxes are low, if they exist at all, and all of the citizens are empowered with rights. They seem to be a perfect libertarian paradise, where the roads get paved and the army keeps everyone safe, but the ruler isn’t building a floating summer home or a giant statue to their favorite deity. The grim truth is that, historically, governments have not really existed for the benefit of the people, but to keep power and money in the hands of a select few.
It’s also true that many GMs choose to gloss over this dimension of their campaign and there’s nothing wrong with that. I happen to think that exploring the themes of taxation, despotism and inequality can add a lot to a game. The downside can be that the players will feel that they are at an unfair disadvantage if they play a member of a group that is part of a definitional underclass, even if it’s only in one part of the world.
Now, obviously you can go in too far with a dystopian setting and the theme presents some special storytelling challenges. Tyrannical settings suffer from the same problem as slave settings: either things change for the better – normally instigated by the PCs – or the entire campaign gets locked into a power balance where the characters have little agency or authority unless they’re playing the bad guys, which opens up a whole separate set of considerations.
Sometimes, there is no winning.
In order to create a facade that will appeal to the people who can help them win the Games, Katniss and Peeta have to pretend to be in love. The people running the Games endorse this for better ratings, even going to far as to change the rules so that two players can win – and survive – as long as they are from the same district. When Katniss and Peeta are the only survivors, the game masters capriciously revert the rules. In response, Katniss and Peeta decide on a mutual suicide pact using poisoned berries that is only stopped by yet another reversal. In the aftermath, both are permitted to live, but they have to maintain the charade of a relationship. Neither of them are happy about the outcome.
The Kobayashi Maru scenario remains one of the trickiest feats for a GM, because you are doing a very bad thing  in order to either advance the story or to prove a point . The thing we can learn from The Hunger Games is that sometimes it’s okay to take away some of the victory or to thwart their goals. This is a very different thing from putting them in a scenario where the only correct plays are to run or submit. In D&D terms, Katniss and Peeta get to keep on playing, but the nature of the game has changed. Would it have been nice for the government to have gotten all warm and fuzzy over their love story and left them to live in peace? Absolutely, but it would have been a different story.
That’s the real lesson of The Hunger Games, that you can win and still not get what you want. The story goes on, but in a different direction. Once you’ve internalized that concept, you have to learn how to find the middle ground. Not giving them what they want creates tension, which is good. Denying the players too much, however, can lead towards resentment. Looking at the reverse, how often you tell the players yes, the real danger is giving them too much and draining out the sense of accomplishment.
Sometimes the good guys are just pawns.
The government uses the hunger games for some specific purposes. First, it reinforces the subjugated status of the people living in the districts. The government forces them to submit to something awful as a reminder of their impotence. The games also reinforce the idea of shame in rebellion.
There’s definitely room in a campaign for a stretch where the PCs lack genuine agency. They might not be subjugated themselves, but they also lack any sort of control or authority. They aren’t Robin Hood. They’re just people trying to get by in a shitty world. The concern with these types of stories is that, sooner or later, the players are going to expect to emerge from the cocoon, so to speak. That’s why you should definitely have an exit strategy.
Freedom is just another word for nothing left to lose.
Many of the characters in the book, particularly Katniss, do things because they don’t feel that they have a choice. Katniss goes beyond the fences because she can’t see another way to survive. She volunteers to take the place of her younger sister in the games. Interestingly enough, Katniss doesn’t kill any of the other Tributes without having been attacked first. Instead, she tries very hard to simply disappear into the forest so as to simply out wait her opponents.
The choices that people make under duress can be excellent fodder for a story, but you have to be careful not to take it too far. You don’t want the players to feel that they are being railroaded or that they don’t have any control.
 I know that there are some simulationists who take exception to the idea that a scene in which the “correct” play is to run away is generally unfun, but I’m not going to proselytize to them. If your players appreciate that particular flavor of chocolate, then by all means serve it to them. I’m just not the guy that can teach you how to do it.
 I think that trying to force your players to see their characters as weak is almost certainly the most dangerous justification for a no-win scenario. Part of the allure of roleplaying is getting to feel things that might not be accessible in “real life.” Taking away that ability to escape can seriously dampen your game and it strongly defines what you’re trying to do as a GM.