There are two concepts that I find very interesting, and that apply to many situations, from everyday life to international politics. One concept applies to prisoners, and the other to Royalty, but their long arms reach much farther.
The "royal" concept is that of the Red Queen's race, taken from Lewis Carrol's Through the Looking-Glass (aka "Alice in Wonderland II"). This race is one in which runners must run the fastest they can to stay in place. To move, they'd have to run twice that fast.
The other concept is that of the prisoner's dilemma. The dilemma is a game with the following rules (taken from Wikipedia):
Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both stay silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So this dilemma poses the question: How should the prisoners act?
The "ideal" solution would seem both to stay silent, but if you look closely, whatever the other player chooses, any single player is better off by betraying. So, any rational player should choose to betray, even though this leads to both betraying, and gives an overall lower payoff (higher punishment for both).
Now, for the third part of the title of this post... why should we care? Well, it seems to me that we can find all around us cases of Red Queen races caused by sub-optimal solutions to prisoner's dilemmas. For example, it is quite apparent the rise in SUVs and all-terrain vehicle sales. People here in Europe seem to start following the silly North-American custom of buying the biggest vehicle available, regardless of usability and needs fulfilled. One of the pseudo-reasons given by sellers is that SUVs are safer. Why would that be? Well, because if a small car and a SUV crash head-on, the passengers of the latter are much more likely to be less hurt than the ones in the former. This sounds rational... but is utter crap. I don't claim that people buy these vehicles for that reason, but it helps.
Now, let's analize the scenario: it is true that in a SUV/small car crash, the SUV is better off. However, SUV/SUV crashes are worse for all passengers than small car/small car hits are. From that information, it is apparent that we are facing a prissoner's dilemma (not counting the fact that SUV/wall hits are also worse). Buying a SUV would be betraying, and buying a small car cooperating. The buyer of a SUV hopes that all other players/buyers get small cars, so that her option gives her an edge over the others. However, if we all think the same, we'll all buy SUVs, and then we will reach a betray/betray equilibrium, when a coop/coop equilibrium would be better for all. We'd be running a Red Queen race, only to end up in the same place: all with SUVs, instead of all with small cars... but all with equivalent vehicles (and actually worse, overall).
Another similar situation would be that of the arms race. We all know the story: two or more countries/factions increase their weaponry, not to be overwhelmed by the other country/faction, in a potential war. Now, no matter what country A does, country B will be better off stocking more weapons: if A stays unarmed, B can beat it. If A arms itself, B has to arm itself not to be beat. However, Both countries being armed (betray/betray) is immensely worse than both countries being unarmed (coop/coop). In both cases the war is deterred by the offensive/defensive equilibrium, but in the former the risk for a catastrophe is much higher.
We are fooled by governments and army leaders, assuring us that other countries will play the "betray" card (and arm themselves), so we should play it too. However, think of the fact that in their countries, the other citizens are told exactly the same about us by their government. An no-one seems to explain that the betray/betray solution is sub-optimal, and that coop/coop solutions could exist.
I have no solution for these issues... but, dear reader, maybe you could find it if you thought about it. Please, do.