Counterintuitive Strategies with Mixed Strategies in Zero-Sum Games

Transcribing some more. And although it certainly started out as a prospect far more interesting than articles about fiduciary duty and ACC law, it's amazing how fast this book about game theory (Games of Strategy, 2nd edition) has gone over my head. I can more or less grasp the idea of Nash equilibrium (although I haven't seen the film, apprently the concept is portrayed hopelessly wrongly in A Beautiful Mind , according to the authors of this text), and thinking about thinking about thinking about thinking is sort of within my reach, but by the time I run into things like:

P[cW+ (1 - c) L] + (1 - p) [aW+ (1 - a)1] = p[bW + (1 - b)1] + (1 - p) [dW+ (1 - d)1]

...(which is much more of a pain in the arse to fix up text-wise than an ordinary English sentence, by the way) my brain really is beginning to glaze over. (Mmmm, glazed brain.)

In the first couple of chapters where I could still keep up however, there was some interesting stuff about situations in which game theory doesn't work. One experiment they came up with was explaining the following rules to two random people: one of the people, A, is given a dollar. Person A then proposes a percentage split of the dollar with Person B, who could either accept this amount, and get that amount of money, or reject it, in which case both people would receive nothing. According to the theory of course, since person A has all the power, person B should accept any offer, as that would get him or her something, which is more than the nothing they will recieve anyway if they reject the offer. Knowing this, and assuming B to be rational, Person A should therefore rationally offer a split of 99 for him or herself, and 1 for person B, and person B should take this. Theoretically of course this makes perfect sense. What they found though, naturally enough, was that Person B tends to go "No, stuff ya" if they think they are not getting a 'fair' amount, and that knowing about this concept of fairness, the most common (unprompted) offer of Person A is 50:50. It was suggested that the amounts of money involved were insufficient to make 'B' people care enough about receiving it; however, they went to Indonesia with the experiment, so although they were putting still relatively small sums in terms of $US up for grabs, to the people they were experimenting with, it was equivalent to about 3 months wages. Although this meant 'B' people might take 60:40, say, they still went 'No, stuff ya' if they thought they were getting too shafted, and 'A' people still offered 'fairer' splits then would theoretically would be expected. There are other similar examples of people being people and deflating the mathematics somewhat (which the authors of the book, to their credit, mostly seem to take this in their stride pretty well, although sometimes there is still a hint of a 'What the...these results don't fit the maths! People are clearly wacky!' sort of reaction). Cool.

Much more important than any of this however is that game theory seems to feature an apparently important concept called complementary slackness. This is highly intriguing to me, as of course TBALC have been expert practitioners of complementary slackness for many years. Having discovered it's an important mathematical concept, I'm wondering if Tim and I can somehow use our extensive expertise in the field to get tenure as maths professors at say, Princeton.

Anyway, I wanted to blog to share some interersting (and indeed, slightly disturbing) spam I got today:

Subject: You Can Be A Cop
Subject: Homeland Security is EVERYONE'S job

Hmmm. Really? Protecting America is everyone's job? Er, not mine, surely? (Possibly Dan's in a year or so, but not mine.) I thought at present I was a casually employed Accessible Formats Processor. Who lived in New Zealand. Presumably it isn't the job of the terrorists, either - or if it is, someone should definitely fire them all, because they're pretty bad at it. I didn't open this message, despite its sort of 'Open now! You may already be a Detective Sergeant!' feel, but I'm wondering if the message contained something along the lines of 'click reply to enrol for your 3 day training course, and qualify to become a Homeland Security Officer! Remember that even if you decide to back out, the 44 Magnum (our Special Gift to YOU) is yours to keep absolutely FREE!!!'

Hmmm. Still, nice to know that I Can Be A Cop. If I like. And now I'd better go, as I'm late for work (I have an anti-aircraft battery at a nuclear power plant to man).

Stories of deepest darkest New Plymouth arriving any day now.