Among the most basic ideas of economics both before and after the game theory revolution is competition with mutual benefits for both competitors. I don't know the intellectual history of the powerful concept, but I doubt very strongly that it originated with the dismal science. Its most natural field of application is politics--incuding war.
For instance, imagine two groups with vastly different goals, both of whom have authority, derived from different sources, share a world. Imagine further that in this world, there is a vast imbalance between both physical and intellectual resources and outcomes material or otherwise. Further imagine that one of the parties is steward to the benifiteers of the resource/outcome imbalance and means to maintain it, while the other means to gain a share of influence for a worldview appealing to very few people that can win neither a democratic nor an economic contest. I can make such an ungainly pile of assumptions without detracting from realism in my model because, as you guess, I actually imagine no part of them.
What will they do? They will fight each other like so many companies, to the benifit of both--but not to the benifit of those who aren't playing. The "aggregate gain in welfare" clause usually tacked on at the end of the article is summarily defenestrated simply because there is no medium of exchange in politics, which playing field helps determine the cultural "value" landscape rather than assuming it, and because the players are offering no product to the public on which their welfare depends, save the imposition of their own worldviews.
Nevertheless, certain principles generally associated with economics apply here. In particular, the continuum of cases from monopoly (monoideology, single player game), to duopoly (duoideology, "clash of civilizations") to oligopoly (the several to many case) to perfect competition (plethora of opinions covering the range of the currently thinkable, open society) should respectively be expected to generate better and better outcomes the more players there are. Except that, again, this market/world can assume nothing: no predetermined product, value, or medium of exchange. Thus, instead of some better than normal profits and some underproduction of a product that remains the same no matter who is producing, we the people, members of the general public and thus bearers of general welfare, get a vast under-production of public ideas which de-legitimates the ideas we are ourselves still quite capable of producing. You're in, you're out, or you're crazy. That clause is the platform on which the maniacs American and pan-Islamic fight each other while we watch. The public, of course, pays the entrance bill. The World Pseudo-Wrestling Federation competitors all get paid, and the winner is, needless to say, predetermined. The Bushies win on vast military superiority, and rally a great majority of people with something to lose to their side, on the strength of the vast intellectual superiority of the societies they claim to represent, but from whose science, law, and traditions they have actually divorced themselves entirely. The Bushies get most of what they want, while the weaker party gets a few theocracies here and there and sympathy for itself and disgust for its opponent among the people with nothing to lose. Two lunatic viewpoints have gained respectability, which means they are part of the mental landscape whether we profess to agree with either or not. In my opinion, the ideological idiom's overall shape determines far more than apparently coherent positions taken within its' space. I am sure others disagree and know things I don't, and would like commentary on this point.
I don't think all this merely an explanation of the undeniable fact that the distribution of wealth and power is getting worse. It may be that, but, on account of the culture of what is in part a culture war being determinants of spaces rather than positions taken in pre-established ones, it would be a mistake to use such yardsticks: the numbers have not been constructed.
Why, if my interpretive synthesis is sensible, is no one using game theory analysis of the current war from a more than military stanpoint? The obvious and superficial answer is that the ideas come from economics and are considered so much right-wing filth on that account. I don't buy it, even if in frustration at the difficulty of formalizing the sort of remarks I make offhand, people may bring themselves to think that way on occasion and pronounce the weighty judgement of considering something bullshit. The truth is that, until game-theory logic can assume less pre-established measurement dimensions (wealth, income, power for groups already given) motives, and workable strategies, these remarks are just that--passing commentary. Likewise and more generally, I don't think anyone deeply holds any thought-out version of the opinion that physical science starting with building blocks is the only real science and the only one we will ever need. The social sciences are, it seems, still very young and undeveloped.