Lecture 15 - Backward Induction: Chess, Strategies, and Credible Threats

We first discuss Zermelo’s theorem: that games like tic-tac-toe or
chess have a solution. That is, either there is a way for player 1
to force a win, or there is a way for player 1 to force a tie, or
there is a way for player 2 to force a win. The proof is by
induction. Then we formally define and informally discuss both
perfect information and strategies in such games. This allows us to
find Nash equilibria in sequential games. But we find that some
Nash equilibria are inconsistent with backward induction. In
particular, we discuss an example that involves a threat that is
believed in an equilibrium but does not seem credible.