Thursday, January 14, 2016

Markets and Tournaments

Prices are a way of evaluating options. Given two floor mops, if mop A works twice as well as mop B, then an efficient market ought to mark mop A at twice the price of mop B.

We could put prices on sports teams in just this way. For example, gambling pools should, given enough information, be able to put proper odds on each team in a match or a tournament.

But a tournament is more interesting than a match. Suppose we have a tournament with four teams playing, A, B, C, and D. We might be able to predict with reasonable accuracy which team will win in a match between any particular pair. But that doesn't let us assign any kind of price or value to each team. A might always win against B, and B against C, but it might happen that C always wins against A! In a four way single elimination tournament, the final champion team will depend on the way the tournament is arranged: on how the teams are paired up in the first round, etc.

Given a tournament structure, accurate pairwise odds will map cleanly to accurate odds on the eventual champion. But different tournament structure can easily give a different most likely champion. Teams don't have a universal value, but only relative to the tournament structure.

Decision making in general is a matter of evaluating options. Accurate evaluation depends on understanding the context in which the various contemplated actions will unfold. This is just a manifestation of the unity of emptiness and interdependent origination. The value of a thing is not inherent in the thing but rather is a property of how the thing is situated in its environment.

1 comment:

  1. A buyer and a seller will generally have different perspectives on the value of a commodity. That's exactly why they can agree on a price. The item is worth a bit less than the price for the seller, and a bit more than the price for the buyer. It's the disequilibrium that makes the market work. But normally markets work best with small spreads. Usually some kind of arbitrage will erase any major disequilibrium. But various store and flow capacities may limit arbitrage.

    I am trying to move from a euclidean space to some kind of differential geometry which could even allow non-trivial topologies. This might happen not just in markets but also e.g. in the evaluation of scientific hypotheses. What might make diversity vital?