Consider the following strategic interaction setup that is meant to mimic the U.S.-Soviet Union rivalry in the 1970-80s. Each country can either act as an Aggressive or Restrained actor.

		Soviet Union	Soviet Union
		Restrained	Aggressive
U.S.	Restrained	4,3	0,-2
U.S.	Aggressive	3,3	1,6

(i) Suppose the two countries move simultaneously. Find the Nash equilibrium.

(ii)Now, consider an alternative scenario where the U.S. moves first. Draw the game tree of this sequential game and find the subgame perfect Nash equilibrium; that is, the Nash equilibrium of the sequential game.

(iii)Finally, consider an alternative scenario where the Soviet Union moves first. Draw the game tree of this sequential game and and find the sub-game perfect Nash equilibrium, the Nash equilibrium; that is, the Nash equilibrium of the sequential game.

Please solve this problem accurately and manually (without using chatgbt as it often makes calculation errors and Problems)

Solve each part to the problem accurately and timely. Please provide an explanation for each part of the question and solve every part of this question.