Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 243 — #251
7.5. Induction in Computer Science 243
the max-player has a strategy that, matched with any min-player strategy,
will define a play of G that finishes with a value of at least v,
the min-player has a strategy that, matched with any max-player strategy,
will define a play of G that finishes with a value of at most v.
(b) Prove the Fundamental Theorem for VG’s.
Hint: Assume by induction that each first move M in a game G has a value v M .
Supplemental Part (optional)
(c) State some reasonable generalization of the Fundamental Theorem to games
with an infinite set V of possible payoffs. Prove your generalization.