Ramsey Theory address problems that ask the question “how many elements of some structure must there be to guarantee that a particular property will hold?”  This is the question that I want to know for brokers.  How many brokers must there be for no price wars to occur.

Very interesting ideas.  I liked the one example on wikipedia Schur’s theorem: for any given c there is a number N such that if the numbers 1, 2, …, N are coloured with c different colours, then there must be a pair of integers x, y such that x, y, and x+y are all the same colour