The Prisoner’s Dilemma

It’s a classic thought experiment, mathematical problem and a cause of much philosophical debate. Over the years it has found its way into every sphere of existence from serious lecturing to game shows to, on numerous occasions, real life. It has been argued as being the basis for all religion, and its place in our society. And to think that it, in its purest form, is nothing more than a story about two men in a jail- the prisoner’s dilemma.

The classic example of the dilemma goes roughly as follows; two convicts suspected of a crime are kept in single custody, separated from one another and unable to converse. Both are in fact guilty of the crime, but the police only have evidence to convict them for a small charge, worth a few months in jail if neither of them confess (the ‘cooperation’ option). However, if they ‘rat out’ on their partner, they should be able to get themselves charged with only a minor offence for complicity, worth a small fine, whilst their partner will get a couple of years behind bars. But, if both tell on one another, revealing their partnership in the crime, both can expect a sentence of around a year.

The puzzle comes under the title (in mathematics) of game theory, and was first formally quantified in the 1950s, although the vague principle was understood for years before that. The real interest of the puzzle comes in the strange self-conflicting logic of the situation; in all cases, the prisoner gets a reduced punishment if they rat out on their partner (a fine versus a prison sentence if their partner doesn’t tell on them, and one year rather than two if they do), but the consequence for both following the ‘logical’ path is a worse punishment if neither of them did. Basically, if one of them is a dick then they win, but if both of them are dicks then they both lose.

The basic principle of this can be applied to hundreds of situations; the current debate concerning climate change is one example. Climate change is a Bad Thing that looks set to cause untold trillions of dollars in damage over the coming years, and nobody actively wants to screw over the environment; however, solving the problem now is very expensive for any country, and everyone wants it to be somebody else’s problem. Therefore, the ‘cooperate’ situation is for everyone to introduce expensive measures to combat climate change, but the ‘being a dick’ situation is to let everyone else do that whilst you don’t bother and reap the benefits of both the mostly being fixed environment, and the relative economic boom you are experiencing whilst all the business rushes to invest in a country with less taxes being demanded. However, what we are stuck with now is the ‘everyone being a dick’ scenario where nobody wants to make a massive investment in sustainable energy and such for fear of nobody else doing it, and look what it’s doing to the planet.

But I digress; the point is that it is the logical ‘best’ thing to take the ‘cooperate’ option, but that it seems to make logical sense not to do so, and 90% of the moral and religious arguments made over the past couple of millennia can be reduced down to trying to make people pick the ‘cooperate’ option in all situations. That they don’t can be clearly evidenced by the fact that we still need armies for defensive purposes (it would be cheaper for us not to, but we can’t risk the consequences of someone raising an army to royally screw everyone over) and the ‘mutually assured destruction’ situation that developed between the American and Soviet nuclear arsenals during the Cold War.

Part of the problem with the prisoner’s dilemma situation concerns what is also called the ‘iterative prisoner’s dilemma’- aka, when the situation gets repeated over and over again. The reason this becomes a problem is because people can quickly learn what kind of behaviour you are likely to adopt, meaning that if you constantly take the ‘nice’ option people will learn that you can be easily be beaten by repeatedly taking the ‘arsehole’ option, meaning that the ‘cooperate’ option becomes the less attractive, logical one (even if it is the nice option). All this changes, however, if you then find yourself able to retaliate, making the whole business turn back into the giant pissing contest of ‘dick on the other guy’ we were trying to avoid. A huge amount of research and experimentation has been done into the ‘best’ strategy for an iterative prisoner’s dilemma, and they have found that a broadly ‘nice’, non-envious strategy, able to retaliate against an aggressive opponent but quick to forgive, is most usually the best; but since, in the real world, each successive policy change takes a large amount of resources, this is frequently difficult to implement. It is also a lot harder to model ‘successful’ strategies in continuous, rather than discrete, iterative prisoner’s dilemmas (is it dilemmas, or dilemmae?), such as feature most regularly in the real world.

To many, the prisoner’s dilemma is a somewhat depressing prospect. Present in almost all walks of life, there are countless examples of people picking the options that seem logical but work out negatively in the long run, simply because they haven’t realised the game theory of the situation. It is a puzzle that appears to show the logical benefit of selfishness, whilst simultaneously demonstrating its destructiveness and thus human nature’s natural predisposition to pursuing the ‘destructive’ option. But to me, it’s quite a comforting idea; not only does it show that ‘logic’ is not always as straightforward as it seems, justifying the fact that one viewpoint that seems blatantly, logically obvious to one person may not be the definitive correct one, but it also reveals to us the mathematics of kindness, and that the best way to play a game is the nice way.

Oh, and for a possibly unique, eminently successful and undoubtedly hilarious solution to the prisoner’s dilemma, I refer you here. It’s not a general solution, but it’s still a pretty cool one 🙂

Advertisement

The Offensive Warfare Problem

If life has shown itself to be particularly proficient at anything, it is fighting. There is hardly a creature alive today that does not employ physical violence in some form to get what it wants (or defend what it has) and, despite a vast array of moral arguments to the contrary of that being a good idea (I must do a post on the prisoner’s dilemma some time…), humankind is, of course, no exception. Unfortunately, our innate inventiveness and imagination as a race means that we have been able to let our brains take our fighting to the next level, with consequences that have got ever-more destructive as  time has gone  by. With the construction of the first atomic bombs, humankind had finally got to where it had threatened to for so long- the ability to literally wipe out planet earth.

This insane level of offensive firepower is not just restricted to large-scale big-guns (the kind that have been used fir political genital comparison since Napoleon revolutionised the use of artillery in warfare)- perhaps the most interesting and terrifying advancement in modern warfare and conflict has been the increased prevalence and distribution of powerful small arms, giving ‘the common man’ of the battlefield a level of destructive power that would be considered hideously overwrought in any other situation (or, indeed, the battlefield of 100 years ago). The epitomy of this effect is, of course, the Kalashnikov AK-47, whose cheapness and insane durability has rendered it invaluable to rebel groups or other hastily thrown together armies, giving them an ability to kill stuff that makes them very, very dangerous to the population of wherever they’re fighting.

And this distribution of such awesomely dangerous firepower has began to change warfare, and to explain how I need to go on a rather dramatic detour. The goal of warfare has always, basically, centred around the control of land and/or population, and as James Herbert makes so eminently clear in Dune, whoever has the power to destroy something controls it, at least in a military context. In his book Ender’s Shadow (I feel I should apologise for all these sci-fi references), Orson Scott Card makes the entirely separate point that defensive warfare in the context of space warfare makes no practical sense. For a ship & its weapons to work in space warfare, he rather convincingly argues, the level of destruction it must be able to deliver would have to be so large that, were it to ever get within striking distance of earth it would be able to wipe out literally billions- and, given the distance over which any space war must be conducted, mutually assured destruction simply wouldn’t work as a defensive strategy as it would take far too long for any counterstrike attempt to happen. Therefore, any attempt to base one’s warfare effort around defence, in a space warfare context, is simply too risky, since one ship (or even a couple of stray missiles) slipping through in any of the infinite possible approach directions to a planet would be able to cause uncountable levels of damage, leaving the enemy with a demonstrable ability to destroy one’s home planet and, thus, control over it and the tactical initiative. Thus, it doesn’t make sense to focus on a strategy of defensive warfare and any long-distance space war becomes a question of getting there first (plus a bit of luck).

This is all rather theoretical and, since we’re talking about a bunch of spaceships firing missiles at one another, not especially relevant when considering the realities of modern warfare- but it does illustrate a point, namely that as offensive capabilities increase the stakes rise of the prospect of defensive systems failing. This was spectacularly, and horrifyingly, demonstrated during 9/11, during which a handful of fanatics armed with AK’s were able to kill 5,000 people, destroy the world trade centre and irrevocably change the face of the world economy and world in general. And that came from only one mode of attack, and despite all the advances in airport security that have been made since then there is still ample opportunity for an attack of similar magnitude to happen- a terrorist organisation, we must remember, only needs to get lucky once. This means that ‘normal’ defensive methods, especially since they would have to be enforced into all of our everyday lives (given the format that terrorist attacks typically take), cannot be applied to this problem, and we must rely almost solely on intelligence efforts to try and defend ourselves.

This business of defence and offence being in imbalance in some form or another is not a phenomenon solely confined to the modern age. Once, wars were fought solely with clubs and shields, creating a somewhat balanced case of attack and defence;  attack with the club, defend with the shield. If you were good enough at defending, you could survive; simple as that. However, some bright spark then came up with the idea of the bow, and suddenly the world was in imbalance- even if an arrow couldn’t pierce an animal skin stretched over some sticks (which, most of the time, it could), it was fast enough to appear from nowhere before you had a chance to defend yourself. Thus, our defensive capabilities could not match our offensive ones. Fast forward a millennia or two, and we come to a similar situation; now we defended ourselves against arrows and such by hiding in castles behind giant stone walls  and other fortifications that were near-impossible to break down, until some smart alec realised the use of this weird black powder invented in China. The cannons that were subsequently invented could bring down castle walls in a matter of hours or less, and once again they could not be matched from the defensive standpoint- our only option now lay in hiding somewhere the artillery couldn’t get us, or running out of the way of these lumbering beasts. As artillery technology advanced throughout the ensuing centuries, this latter option became less and less feasible as the sheer numbers of high-explosive weaponry trained on opposition armies made them next-to impossible to fight in the field; but they were still difficult to aim accurately at well dug-in soldiers, and from these starting conditions we ended up with the First World War.

However, this is not a direct parallel of the situation we face now; today we deal with the simple and very real truth that a western power attempting to defend its borders (the situation is somewhat different when they are occupying somewhere like Afghanistan, but that can wait until another time) cannot rely on simple defensive methods alone- even if every citizen was an army trained veteran armed with a full complement of sub-machine guns (which they quite obviously aren’t), it wouldn’t be beyond the wit of a terrorist group to sneak a bomb in somewhere destructive. Right now, these methods may only be capable of killing or maiming hundreds or thousands at a time; tragic, but perhaps not capable of restructuring a society- but as our weapon systems get ever more advanced, and our more effective systems get ever cheaper and easier for fanatics to get hold of, the destructive power of lone murderers may increase dramatically, and with deadly consequences.

I’m not sure that counts as a coherent conclusion, or even if this counts as a coherent post, but it’s what y’got.