19 June 2006

Wikiepedia and Abstract Strategy Games

Last night when I got home, I recounted to my housemate what I did: NBA Finals, beer, poker and speeches. It then occured to me that young men have changed little since 399BC; still there are drinking parties, serving girls and speeches made. The casual man-boy butt love has since taken its act more underground, but mostly things are the same. We gather around, arrayed all on our cushions and pillows, get drunk and make speeches. Last night our speeches were about whether chess is like blackjack. Can the human have perfect knowledge? And finally, battery-operated disposable razors--what the fucks up with that?

A young slave boy remembered hearing about a particular speech about chess from his deaf grandmother who had whelped him. She heard it from a gardener who happened to be mowing the lawn while some men were talking; but they got fed up with his incessant lawn mowing while they were making speeches and kicked him out. Frame within a frame within a riddle! The speech began innocently enough.

The NY Times generated this article a few days ago outlining Wikipedia's protecting certain entries from being edited. It is conceivable that much more of Wikipedia could become protected, which more or less means that they were given a whole lot of information for absolutely nothing.

To take a little from Wikipedia regarding Chess, an abstract strategy game,

The analysis of a "pure" abstract strategy game tends to fall under combinatorial game theory. Abstract strategy games with hidden information, bluffing or simultaneous-move elements are better served by Von Neumann-Morgenstern game theory, while those with a component of luck may require probability theory incorporated into either of the above.

which shows at least one thing: There are two modes of operation depending on your given information i.e., your epistemic conditions. On the one hand, given "complete information", you're advised to use combinatorial game theory; however, given hidden information", then the advised operating mode is Von Neumann-Morgenstern game theory. (That John Von Neumann is probably the most brilliant person of the 20c--no shit. Areas given his profound effect: Logic, set theory, computer science, quantum theory, game theory and economics. Read any history of math in the 20c.-type book, and a lot of 20cBooksks about science, and I guarantee that Von Neumann will figure in the book.) But it has been suggested that the human himself lacks complete information, even in a game that allows for complete information. In this sense, even while playing chess one operates in an epistemic condition that calls for the application of probabilistic game theory-type thinking. Does the prisoner's dilemma map onto the playing of chess?

I think not. There are at least two paradigms for the application of game theory cooperative and noncooperative games. Depending on how one looks at it, he could consider a cooperative situation as one in which he is encouraged to act such that the group's situation is optimized, i.e., the cartel system or the prisoner's dilemma. Then there are game theory situations in which one wants to win—noncooperative games--and thus he tries to predict his competitors' actions, i.e., the blonde-situation in A Beautiful Mind. In that scene, Russell Crowe qua John Nash is in a bar with his buddies and they spot a hot blonde. He tells them not all to go for the blonde because then none of them would get her. This is a noncooperative game. I quote:

A Nash equilibrium is not necessarily a "best solution" nor does it necessarily give the "best result". Nevertheless, at such an equilibrium, no player is motivated to change his (mixed) strategy since he cannot force other players to change theirs. [...] [T]he theory of noncooperative games assumes that each player does what is "best for himself", regardless of what is best for "the group".

I don't know much about logic or game theory, but this all implies to me that the above describes the metastases of participants' strategies in various competitive situations. The important distinction, though, is that these situations are all and only of the type in which you cannot predict another's move (i.e., incomplete information). That's why a Nash equilibrium doesn't necessarily give a 'best solution', etc.

In chess, again, I'd say there is complete information, and there is always a best solution. If I know that the blonde dislikes non-doctors and the brunette likes lawyers, and I, a doctor and my buddy who is a lawyer, are out at a bar--then I would know the best strategy. But given that people don't walk around wearing sandwich boards listing their social preferences, we have to make small talk, lie, feed people alcohol etc in order to get anywhere. The social preferences of chess pieces are embedded in the rules of the game. Even to play chess is to partake in the notion of a best move. We don't wear epistemic blinders that limit our understanding of the game, as if at one moment I forget that the knight moves in an L-shape and at another I confuse my bishop for my rook. By playing chess under normalized, agreed upon rules we admit a best move; if we didn't then Bobby Fischer would occasionally lose to a scrub. That is the logical conclusion.