The question I want to investigate in this post is: “Is the Hunger Games universe in a game-theoretic-Nash-equilibrium?”
The first game seems to be a variant on the tragedy of the commons. Assume every kid in District 12 has two options: “get food” or “don’t get food”. If they get food, they eat better, but have higher chances to get selected as a tribute. Assume that every kid who gets food as twice as much chance to get selected as a kid who does not. In this case, assuming nobody is starving, everyone will choose the “Don’t Get Food” option, because it always halves their chances of being selected — even though if they all chose the “Get Food” strategy, they would all have been better off. There is a standard way to get to the best option in the tragedy of the commons game — “burn utility by a higher power” or, in layman’s term, enact a law. This is what district 2 does — the district chooses people at birth for the hunger games. However, we could also use a variant of Desirism — without enacting it into a law that a pair has to go into hunger games, cast a lottery each year for the babies born that year, and then train them and instill in them a desire to volunteer when “their time comes” (say, at age 15). These kids go to their death, the lottery is still enacted, but then these kids volunteer instead of the lottery losers. This way, everyone can take as much food as they want — basically, food would become a free commodity. Since the model of District 2 is there to learn from, clearly the leaders of every other district are morons.
Furthermore, that would be a stable equilibrium from the point of view of the districts as rational actors. Every district would have the two options: “Groom champions” or “Use a random lottery”. Any district that chooses the random lottery option will significantly hamper their chances at winning. Therefore, there is a distinct advantage for districts to go with the “Groom champions” strategy.