(War)Game Theory

Every once in a while I flick through my big book of philosophical terms looking for something that might be interesting to write about. This usually occurs, of course, when I have not thought of or found anything else, so it is sort of my ‘scraping the bottom of the barrel’ or desperation activity. And so this time I came across an article about ‘game theory’, and the thing that caught my eye was the assumption it makes about the other players all being rational.

Game theory is not, of course, about game, or at least wargames as we would like to know them as an interesting and enjoyable pastime. Game theory is actually a bit of mathematical logic about outcomes. A paradigm case would be of two soldiers, Dan and Tom. They are ordered to stay at their posts. However, they also know that if both run away, then the enemy will break through and their chances of survival will be minimal. If one stays at the post, their chance of survival will be small, but the other, who will run away, will have a good chance. If they both stay, they both have a reasonable chance of survival.

If the two soldiers are in ignorance of the choices of the other, and assuming that both parties are acting rationally, they will, of course, both run away. The way the mathematics works is that given the symmetry of the situation, the biggest payoff is by running.  If the other runs, then I will not survive. If the other stays and I stay, I will not survive. Therefore, the best is to run and hope that the other stays. The scenario where both decide to stay on the off chance that the other will too is not strictly rational, for if the other stays, I will have a better chance of survival if I run. This is, of course, a form of the prisoner’s dilemma.

The scenario assumes, of course, that both Tom and Dan make rational choices and they do not enter an agreement about staying. If they do enter such an agreement, the dilemma then becomes one about trust, virtue and ethical morality, and moves a little way outside strict game theory, although the logic can be modified to account for the collusion between the players.

What game theory does not account for, of course, is the hero. The hero would stay whatever the circumstances, holding the post for his colleagues to run away. The hero, for whatever reasons, breaks the strictly rational assumption of game theory: he does not behave in a rational manner. A normal solution to a game theory scenario is that each (rational) agency will maximise the utility of the situation given other rational agent’s strategies. The hero breaks that; he is not out to maximise his own utility, or at least, his calculation of utility differs from the other rational agents. The hero is thinking, perhaps, more in terms of fame, glory or honour, while his colleagues (who presumably gratefully run away) are thinking in terms of utility being saving their lives.

The hero’s course of action is, in some world views, entirely logical. If returning from a battle with your life intact but your reputation in shreds is, for you and your world view, an unbearable stain on you and your family, then it is likely at your rational utility calculation will be different from Tom and Dan’s. Or at least, if you do run away, you might make sure you are the first into combat in the next battle, to try to regain your reputation.

The point of all this is to suggest two things. Firstly, that our own sense of rationality might not be that of our toy soldiers. Often, as wargamers, we make decisions for them which accord with our own, modern Western rationality. This rationality usually (although not always) argues for the preservation of my life. Thus, for example, various rules of engagement assess the threat to the participants before permitting using lethal force. We can, therefore, force our little lead warriors to act outside their own world-view. It might be rational for the Spartans to retire, but would they really do it? History suggests that the answer is ‘no’.

Secondly, of course, is that the ‘cold’ rationality of game theory is not actually how we, as humans, think, at least, not all of the time. We can set up our soldiers with all due knowledge of history, the capability of the forces, the enemy, the terrain, and the rules and so on. No one, however, can make us do so. We do this because this is how the rules, history, the nature of wargaming and so on have conditioned us. We could simply grab a unit and plonk it onto the table in any order. But we do not. We impose an order, a rationality upon it.

We assume, furthermore, that our opponent is equally rational. He, too, is placing units on the table with due regard to all the constraints and opportunities available to him in the circumstances. During the wargame, we move our forces, open fire and so on, again, with due consideration and rationality, assuming that our opponent is doing the same. In fact, in many rule sets, there are special rules to ensure that our soldiers, or at least their officers, are not acing with such rationality. Thus in DBM, I seem to recall, there were irregular knights whom, at the throw of a dice (I think it was something to do with not issuing a command a turn to stay in place) zipped off to charge the nearest enemy unit. Similarly in Tercio and the old WRG Gush Renaissance Rules there were ‘A’ class troops (or, in Tercio, M1 troops) whose main activity was to charge the nearest foe. Somehow, we have rationalised the irrational decisions of our troops.

Nevertheless, I suppose that our assumption that our opponent is rational is, um, rational. But it is not necessarily so. And, of course, an apparently irrational move could make perfect sense to our opponent. It turns out, for example, that the impetuous charge of Royalist cavalry in some actions of the ECW was perfectly rational: it was designed to sweep the enemy away as they (the enemy) were often present in greater numbers. In this case, the troops simply need to be classified as rational, not A class impetuous upper class twits.