Confuseling
Irreligious fanatic
- Joined
- Feb 26, 2008
- Messages
- 1,243
I've been thinking about writing a little discussion about game theory and secret societies. I couldn't be bothered to draw the table, because I'm inherently lazy. To my immense displeasure, I have discovered
the | table | feature and run out of excuses.
Game theory
Game theory is a concept fundamental to modern economic thought. It describes decision making with limited information. The archetypal game, known as the Prisoners' Dilemma, brilliantly illustrates the difficulties in achieving collective action.
Prisoners' Dilemma:
| | |
Player B
| | cooperate | defect
| cooperate | 1, 1 | -3, 2 Player A | defect | 2, -3 | -1, -1
It looks confusing (Christ, you should see the bbcode
), but you have nothing to fear. The situation is as follows. Two miscreants have been caught in a crime. They are about to be interrogated separately. Honour among thieves, when it comes to the crunch, isn't all that honourable; each seeks only to maximise their own score. The rules are very simple. Each player plays simultaneously - which is to say that they don't know their opponents choice when they play. They have two options - they can agree to cooperate, and pretend to know nothing about the crime at all, hoping to get off with a light sentence. Or they can defect, and tell the police all about their misdeeds, securing their opponents conviction in exchange for a plea bargain.
Imagine we are player A. Our two choices are marked by the two rows - first cooperate, then defect. Our scores are written in red, followed by player B's in blue. Each row contains two columns, representing the eventualities of player B's choice if we choose this row - first cooperate, then defect.
In order to analyse the game, we effectively use backward induction - reasoning backwards from our opponent's choice. If player B were to choose to cooperate, we would choose from the first column - either 1, 1 if we cooperate, or 2, -3 if we defect. Remember, we are entirely uninterested in our opponents score - we seek only to maximise our own. Clearly we are better off defecting. What if they choose to defect? Second column, we get -3, 2 if we cooperate and -1, -1 if we defect. It transpires that we are in fact better off betraying our erstwhile comrade irrespective of their choice.
The game is symmetrical, so player B necessarily follows the same logic. Here lies the eponymous dilemma: we both prefer the solution in which we remain quiet, but through rational self interest we confess, and betray one another.
Iterative game theory
A bleak and hollow vision, with little relation to real behaviour? Perhaps. We may in fact sometimes be glad people don't listen to the models - Von Neumann, one of the early game theorists, counseled that the best course of action was full preemptive nuclear warfare against the Soviet Union, which would, it must be assumed, have been a mess. Social reality isn't an all or nothing stand-off, fortune has it, but rather a continual process of negotiation.
Continuing the logic of backwards induction, what happens if we play multiple times? Suppose we are going to play ten games. We start from the assumption that we are best off cooperating throughout, but I know that I'm better off in the last game defecting, because you can't punish me afterwards. You are beholden to the same logic, and as you intend to betray me in the last game, I have no interest in 'playing nice' and cooperating in the second to last in order to secure future favour. We work backwards, and realise we are exactly where we started - stabbing each other relentlessly in the back.
What, however, if we play the game an infinite or unknown number of times? We can't induct backwards from an unknown point, so things get interesting. As long as we believe that betrayal will induce counter-betrayal, we are best off trying to secure continued mutual cooperation and building trust.
Implicit collusion
So let's apply this to a real world situation - that of supermarket price-wars. Both supermarkets are better off cooperating to keep prices high, but either will gain in the short term by cutting them, taking their opponent's customers. If continued, this will inevitably induce reciprocal cuts, equalising the losses, until someone balks and a new round of cooperation ensues. We can envisage the extra points tempting either player into betrayal gradually increasing, as the profit margin, and thus the potential scope for slashing prices, gradually drifts upwards, until a snapping point is reached, and somebody starts a new round of price-wars.
The interesting thing about price-wars is when they don't happen. The very fact that a spate of reciprocal cuts suddenly occurs is indicative of a period of cooperation beforehand, during which potential cuts were foregone; otherwise, prices would forever remain flat at the minimum cost of production and distribution. Supermarkets, in a highly competitive field and with no overall capacity to consciously coordinate their actions, manage to operate this ethereal cartel for sustained periods; a process known as implicit collusion. The fact that there are many of them does not alter the fundamental logic of the situation - it's just easier to draw the chart in two dimensions.
Secret societies, William of Ockham, and Capital
This framework gives us a very simple, but surprisingly powerful way of analysing decision making in the face of unknown behaviour on the part of other actors. The smaller the number of players, the higher the probability of sustaining cooperation for sustained periods. We can explain the apparently coordinated behaviour of politicians, firms, even nations themselves by appeal to the notion of implicit collusion - heads of state and business do not need smoke filled rooms to apparently spontaneously decide en masse to reconfigure strategy or legislation; they can rely on continued profiteering as the cold logic of the shared motivator. The fact that they appear to dance in concert reflects the precarious nature of their position and the vicissitudes of the market, finely balanced between the conflicting interests of capital and labour (a conflict itself modelable as a game), and flocking according to subtle variations in their opponents strategies. Secret societies exist; there is absolutely no doubt about that - occasionally we discover one, and they seem to come from somewhere
. But in the vast majority of cases their invocation adds no explanatory value, and we may be certain of this particularly by the fact that whenever a culture is wrenched open to external scrutiny by rapid disintegration or conquest, they have played no functional part in its structure beyond that of spectres disguising the fundamental imperatives of class. They are part of the political mythos, borne of the same error in reasoning that caused our ancestors to worship the weather; the attribution of intentionality to explain - or to tame - threatening patterns. Superstition and magical thinking are a heavy veil to lift, but you can survive perfectly well without them. As William of Ockham had it: do not multiply entities beyond necessity.

Game theory
Game theory is a concept fundamental to modern economic thought. It describes decision making with limited information. The archetypal game, known as the Prisoners' Dilemma, brilliantly illustrates the difficulties in achieving collective action.
Prisoners' Dilemma:
| | cooperate | defect
| cooperate | 1, 1 | -3, 2 Player A | defect | 2, -3 | -1, -1
It looks confusing (Christ, you should see the bbcode
Imagine we are player A. Our two choices are marked by the two rows - first cooperate, then defect. Our scores are written in red, followed by player B's in blue. Each row contains two columns, representing the eventualities of player B's choice if we choose this row - first cooperate, then defect.
In order to analyse the game, we effectively use backward induction - reasoning backwards from our opponent's choice. If player B were to choose to cooperate, we would choose from the first column - either 1, 1 if we cooperate, or 2, -3 if we defect. Remember, we are entirely uninterested in our opponents score - we seek only to maximise our own. Clearly we are better off defecting. What if they choose to defect? Second column, we get -3, 2 if we cooperate and -1, -1 if we defect. It transpires that we are in fact better off betraying our erstwhile comrade irrespective of their choice.
The game is symmetrical, so player B necessarily follows the same logic. Here lies the eponymous dilemma: we both prefer the solution in which we remain quiet, but through rational self interest we confess, and betray one another.
Iterative game theory
A bleak and hollow vision, with little relation to real behaviour? Perhaps. We may in fact sometimes be glad people don't listen to the models - Von Neumann, one of the early game theorists, counseled that the best course of action was full preemptive nuclear warfare against the Soviet Union, which would, it must be assumed, have been a mess. Social reality isn't an all or nothing stand-off, fortune has it, but rather a continual process of negotiation.
Continuing the logic of backwards induction, what happens if we play multiple times? Suppose we are going to play ten games. We start from the assumption that we are best off cooperating throughout, but I know that I'm better off in the last game defecting, because you can't punish me afterwards. You are beholden to the same logic, and as you intend to betray me in the last game, I have no interest in 'playing nice' and cooperating in the second to last in order to secure future favour. We work backwards, and realise we are exactly where we started - stabbing each other relentlessly in the back.
What, however, if we play the game an infinite or unknown number of times? We can't induct backwards from an unknown point, so things get interesting. As long as we believe that betrayal will induce counter-betrayal, we are best off trying to secure continued mutual cooperation and building trust.
Implicit collusion
So let's apply this to a real world situation - that of supermarket price-wars. Both supermarkets are better off cooperating to keep prices high, but either will gain in the short term by cutting them, taking their opponent's customers. If continued, this will inevitably induce reciprocal cuts, equalising the losses, until someone balks and a new round of cooperation ensues. We can envisage the extra points tempting either player into betrayal gradually increasing, as the profit margin, and thus the potential scope for slashing prices, gradually drifts upwards, until a snapping point is reached, and somebody starts a new round of price-wars.
The interesting thing about price-wars is when they don't happen. The very fact that a spate of reciprocal cuts suddenly occurs is indicative of a period of cooperation beforehand, during which potential cuts were foregone; otherwise, prices would forever remain flat at the minimum cost of production and distribution. Supermarkets, in a highly competitive field and with no overall capacity to consciously coordinate their actions, manage to operate this ethereal cartel for sustained periods; a process known as implicit collusion. The fact that there are many of them does not alter the fundamental logic of the situation - it's just easier to draw the chart in two dimensions.
Secret societies, William of Ockham, and Capital
This framework gives us a very simple, but surprisingly powerful way of analysing decision making in the face of unknown behaviour on the part of other actors. The smaller the number of players, the higher the probability of sustaining cooperation for sustained periods. We can explain the apparently coordinated behaviour of politicians, firms, even nations themselves by appeal to the notion of implicit collusion - heads of state and business do not need smoke filled rooms to apparently spontaneously decide en masse to reconfigure strategy or legislation; they can rely on continued profiteering as the cold logic of the shared motivator. The fact that they appear to dance in concert reflects the precarious nature of their position and the vicissitudes of the market, finely balanced between the conflicting interests of capital and labour (a conflict itself modelable as a game), and flocking according to subtle variations in their opponents strategies. Secret societies exist; there is absolutely no doubt about that - occasionally we discover one, and they seem to come from somewhere
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