14.5.03

RUNNING LIONEL ON SCALE TRACK? Professor Farrell takes advantage of the conclusion of "Survivor" to spin a parable about network theory as a way of understanding human conflicts that has some advantages over game theory. This commentary from Professor Healy provides some additional background. But chess as somehow isomorphic to the Florentine Courts? In principle, chess is solved. There is a final move. It is either a draw, a win for White, or a win for Black. Therefore, there is a sequence of moves by which White can force a win, Black can force a win, or Black can force a draw. However, nobody has demonstrated either of the first two outcomes (players keep finding improvements in lines unfavorable to either side, which is a good way to sucker your less-informed opponent into a false sense of security, you lead him into the previously favorable-for-him variation and whack him with the improvement.) Perhaps for each possible opening move by White there is a drawing move for Black, but there is no easy way to prove that conjecture. Similarly, for each "Survivor" cast member, there is a final move. You get voted off, or you don't get voted off. Therefore, there must be a sequence of strategies by which some player can force a victory. Indeed, "Keep your end-goals and specific strategies mysterious - try to be all things to all men and women. Maintain flexibility at all costs. And then go for broke when the opportunity arises" has similarities to luring your opponent into the favorable-for-him variation and then springing your prepared move. The courts of Florence pose a slightly different problem as it isn't clear what each courtier's objective is.

Methinks my finished-with-finals (true here as well) colleague goes a bit too far taking digs at economics and "Survivor." One could look for the mixed strategies, or the option value in using your immunity challenges, or tossing them to someone else, but somehow looking for deep insights into a contrived conflict designed to showcase Thirteenth Generation crudities (or am I thinking about baseball?) is less constructive than looking for the evolution of cooperation among purposeful individuals who might be revising their objectives in light of new information and with the responsibility of developing the rules as they go.

UPDATE: Professor Farrell has a bit more here including the useful argument that in a sufficiently complex problem (such as working out variations in a quiet position or participating in a one-and-done reality show), "[h]ighly complex games are more or less equivalent to indeterminate ones from the point of view of human beings, who have limited mental processing power." Quite so. The puzzle about whether or not chess has a solution goes into territory where I don't dare tread. Let's suppose that a sufficiently powerful algorithm can verify the folk version of the Zermelo conjecture (which I am treating somewhat less restrictively as a potential existence proof) and chess players everywhere will have to take up sheepsheadinstead). Per analogy to the four-color map conjecture, there are likely to be those mathematicians who will not accept an unbeatable (but does no better than a draw against proper play) chess algorithm as demonstration of the solution whose existence is suggested by the Zermelo conjecture.

I too am done with this particular story, as sailing season approaches.

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