Answer Happy

3. The countries of Gassia and the United Shire of Anglicans
(USA) are playing a dangerous game! Gassia threatens to invade
Ubraine, one of the USA’s allies. However, the USA gets to move
first. It can place its army in Ubraine (Place) or stay out (Out).
After that, Gassia can decide to invade (Attack) or stay out (Out).
Finally, if the USA stays out and Gassia invades Ubraine, the USA
can decide to levy sanctions that will hurt both of them
(Sanctions) or to do nothing (Nothing). If they both stay out and
there is peace, the payoffs are (10, 10). If they attack each other
and there is war, the payoffs are (- 20, - 20). If the USA stays
out and Gassia invades, the payoffs are (8, 14) without sanctions
and (7, 12) with sanctions. The first number is the payoff for the
USA and the second for Gassia. a) Show this game using a
well-labeled game tree. b) How many subgames are there in this
game, and what is the Subgame Perfect Nash Equilibrium. Explain
why. c) Are levying Sanctions or going to War credible threats?
Explain. Why is (Out; Invade; Sanctions) a likely outcome even
though it is not an equilibrium?