Saturday 6 June 2015

(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.


  1. Good stuff - I'm not sure I am altogether pleased with the idea that, in addition to the damned dice having a malicious tendency, the little soldiers might be awkward sods as well.

    I'm not sure whether doing something unexpected to surprise the enemy (i.e. something opposed to the logic, or the logic of what he expects me to expect, or what I expect him to expect I am expecting...) just drops into your main development here - shades of primary school kids defeating a more experienced chess player simply because they have not studied the classic moves, and do not carry out the "correct" moves.

    The upper class twits ECW thing is interesting, as well. I read somewhere that the caracole and all that nonsense only worked when only the upper class twits had pistols, and theoretical military posturing was the mark of a gentleman. The idea then was that Gustav Adolfus and his mates decided that the pistol as a state-of-the-art weapon wasn't nearly ready for all this carry-on, and it was a good idea to forget about it and just charge at the pistol-strugglers to try to put them off their stride (or whatever). Speaking of which, I recently introduced a rule disaster in my home-brewed ECW game whereby I gave "galloper" type horse extra combat dice for striking the first blow in a melee, which accidentally encouraged the trotters to take the initiative in each combat, to remove this bonus effect, and thus we briefly had the most aggressive trotters ever seen. The wargames rules changed history - can't have that - interesting to think of trotter berserkers in game theory terms. No-one expected that...

    1. The caracole is a bit of an odd thing in military history, I find, if anyone can actually give an example of its use in action I would be interested, but usually it is referred to in the past tense as 'this is what cavalry used to do, but modern tactics have superseded it'.

      But yes, I'm afraid that your dice, your toy soldiers, the terrain and, to some extent, your enemy are against you. I often find that illogical moves are the most logical, in retrospect...

  2. I have known some very irrational wargamers in my time (as have some of my friends perhaps). People hold grudges, or superstitions or have favorite units that they favor for emotional reasons or vice versa.

    But in some circumstances what appears as illogical is merely a question of differing facts, suppositions or goals. I may not be aware of a special scenario victory condition for the other side, my opponent might be new to the period and not have grasped the difference between phalanx and peltasts, etc

    Military questions are also affected by discipline and training is brain washing or conditioning which changes what seems right or even possible. This affects the dilemma as good training has taught the 2 veteran soldiers (rightly or wrongly) that both staying is safer than running, it becomes an unspoken shared belief rather than colludion. This is different from the conscript or the hero. Of course st some point fear can still over come training but that I'd emotion not logic.

    I admit I like games that leave as much as possible to the logic and emotion of the players rather than letting them hide behind the dice driven failures of their little men.

    1. I think a lot depends on world-view. Early Europeans really moaned about the 'skulking way of war' of native North Americans. They did not stand up to be shot like proper armies; a bit of a culture clash.

      I do recall that someone once said the best way of winning a wargame was to convince your opponent that he was losing; then he did. It doesn't work with solo games, however.

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  4. {\rtf1\ansi\ansicpg1252
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    \f0\fs26 \cf2 \cb3 \expnd0\expndtw0\kerning0
    \outl0\strokewidth0 \strokec2 Your post reminded me of a comment Conrad made about a criticism of "Lord Jim". The critic said that the book was absurd and totally unbelievable - Jim should just leave. Conrad's response was that he wondered if the lady in question even knew what honour was? \
    An instructor of mind told us once that the most dangerous period in any arrest was the assessment phase preceding the use of force. Essentially this boils down to working out exactly what kind of fight one has landed in. Old lags are very easy to deal with, but the real problem is juveniles and yhe mentally ill. They have no sense of proportion and always escalate the situation generally because they perceive the conflict as an existential one, rather than what is actually occurring. \
    With regard to the upper class twits. If I recall it was quite a successful tactic for a while at least. Attack a la outtrance may be the rational act under the circumstances. }

    1. In game theory it probably would be rational for the unit to make such a charge as it gives the best chance of a good outcome (and probably the best chance for as many of the unit's members to survive). I guess when you break it down to the individual level it's then a question of how each man sees what is the best outcome for him which is where things like honour, solidarity, esprit de corps, training and simply how they're feeling on the day come in. To me this would lead towards allowing the wargamer less control over units than is often the case in rules.

      "Are we to stand here and be shot like dogs?"

    2. Comment about what kind of fight reminds me of a friend of mine who made his living in what at the time were called "discos" - security and "bouncers" were an important part of running places full of drunk young men. He reckoned the gangs of toughs from the schemes were less of a problem than the respectable nights-out from the local rugby club, since the rugby types had not served their apprenticeships on the streets, and did not understand the rules - if anyone ever got killed, or a place got seriously wrecked, it would always be the better-class boys that lost the plot.

      Me, I used to stay at home with a book.

    3. Oh yes; if everyone obeys the rules, no one need get hurt. It is the fanatics, the untrained and the unschooled who cause problems. I think in Shaw's 'Arms and the Man' the upper class twit character (I think his name was Sergius?) declares that he has not got a promotion because he won the battle in the wrong way (a cavalry charge on machine guns) while the generals were losing it in the right way.

      I'm not sure how most wargamers would react to having less control than now over their units. I tend to find that they are hard enough to direct as it is....

    4. Apologies for this - I do not wish to clutter your blog post, but my head is buzzing, once again. If we dumb down the concept of game theory to a more accessible idea of "what is the best thing to do in the circumstances?" then it very obviously depends on

      (1) define best - from whose point of view - etc

      (2) all the subjective, received stuff like honour, patriotism, keeping up appearances, religion, ideology - all that - confuses the matter, and it becomes increasingly subjective, and things like orders and accountability become important

      (3) a big issue is, "how reliable is our data? - how confident are we in our estimates?" - a slice of this is how personal and how immediate are the consequences. Tom and Dan will have a lot to think about, but somewhere in there will be a subjective balance between (a) I am going to get killed very painfully, versus (b) the empire/state/whatever might just fall as a result of my running away. Since (b) seems further away, of uncertain form and diluted by an expanding funnel of collective responsibility, it would take a remarkable soldier to see past (a). OK - define remarkable, quite.

      I have done some formal study of risk management theory in my day, both from an actuarial point of view and from fund modelling and project management - it was very interesting, but one observed rule of thumb was the deeper you went the flakier became the assumptions you were forced to make (not unlike the illusion of realism in complex wargame rules?). As you can tell, I claim no real expertise, but two thoughts loom large in my mind:

      (1) I once resigned from a management team in a commercial environment when they minuted the fact that they considered it better to fail by not correcting an inherited problem than to fail by attempting an unsuccessful fix and thus being directly, and more obviously, accountable. We can deduce a number of things about the context - one is that that team did not believe that their lives could be ruined by a corporate failure...

      (2) All those guys that went over the top in WW1 - I'll get into terrible trouble if I even accidentally hint that they were anything other than heroic patriots, so I shall not go there, but somewhere, however far down it might be, must have been a consideration of the comparison of probably being killed or maimed by exposing oneself to enemy fire as against an absolute certainty of being shamed and executed if one refused to go. All the other stuff about honour and letting one's mates down is in there as well, of course, I hasten to add, before Kinch the Royalist cop gets after me.

    5. One of the things I find is that few people actually evaluate their data. It seems to be along the the lines of I know X and Y, so I'll do Z, where X and Y might be true, but dependent on viewpoint A, which not not that of the decider. Thus the results can be unpredictable, even if the decider is acting rationally.

      I think Wellington's remarks about making knots might be relevant, as well; the implication seems to be that he thought Boney's plans were fine if it all went right, but hit problems if the enemy didn't do the expected thing.

      My experience of management is no better than your's; experience in blaming someone else is required. As for WWI, I think that a lot of people must have thought going over the top futile, at least until 1918's combined arms tactics came along. But all the way up and down the command chain, there was not much else that could be done. The 1916-7 battles were significantly caused by politics, not strategy.

      But please don't worry about cluttering blog posts; the comments are great and give me other ideas so I don't have to resort to my big book of philosophy again.