PART B - BASIC POTENTIAL TECHNIQUE – GAME-THEORETIC FIRST AND SECOND MOMENTS

Summary

Part B is a practice session for the potential technique, demonstrating the enormous flexibility of this technique.

We look at about a dozen amusing “little” games (similar to the S-building game in Section 1). There is a large variety of results, starting with straightforward applications of Theorem 1.2 (“building”) and Theorem 1.4 (“blocking”), and ending with sophisticated proofs like the 6-page-long proof of Theorem 20.3 (“Hamiltonian cycle game”) and the 10-page-long proof of Theorem 15.1 (“Kaplansky's Game”).

The core idea is the mysterious connection between games and randomness. By using the terms “game-theoretic first moment” and “game-theoretic second moment,” we tried to emphasize this connection.

The point is to collect a lot of “easy” proofs. To get a “feel” for the subject the reader is advised to go through a lot of easy stuff. Reading Part B is an ideal warmup for the much harder Parts C-D.

A reader in a big rush focusing on the exact solutions may skip Part B entirely, and jump ahead to Sections 23–24 (where the “hard stuff” begins).