This chapter provides a game-theoretic analysis of extended deterrence, in which a defender country is trying to deter an attacker country from attacking an ally of the defender. The focus is on how incomplete information on the part of the attacker country can lead to an unwanted war between the attacker and defender, and how a high- resolve type of defender can credibly signal its high resolve so that the attacker is deterred and an unnecessary war does not occur. The signaling mechanisms analyzed include costless messages (“cheap talk”), public threats that generate domestic audience costs for backing down, military mobilization, and risky signals such as threats that leave something to chance. It also analyzes signaling on the part of the ally, and how costless messages can credibly signal information when the actors have sufficiently aligned interests. The exercises ask the reader to derive separating equilibria, semi-separating equilibria, and pooling equilibria, as well as to do comparative statics on equilibrium results.