1.) In the 1960s, the Soviet Union began moving missiles and military hardware into Cuba. In response tothe aggressive maneuver in the United States' backyard, the US Navy began blockading Cuba and wouldintercept Soviet freighters carrying military hardware and missiles bound for Cuba. The growing tensionhad the Soviet Union on the brink of retaliation against the United States.If the Soviet Union does not move missiles into Cuba, then the US and the Soviet Union receive a payoffof 0. If the Soviet Union does move missiles into Cuba, then the United States has the opportunity torespond. If the US does not blockade Cuba and intercept the Soviet Union's freighters, then the SovietUnion is allowed to establish a dangerous military presence in Cuba leading to a payoff of 5 for Cuba and-5 for the US. If the US does blockade the Soviet Union, the Soviet Union can choose to escalate theconflict and declare war against the US. Since the war would end via mutually assured destruction, theUS and the Soviet's would receive "negative infinity" as their payoff. If the Soviet Union does notescalate and allows its ships to be blockaded, then the US "calls the Soviet bluff" and the US receives apayoff of 10 while the Soviets receive a payoff of -10.

Required:

a.) Model the sequential interactions as an extensive form game. Moreover, define the action space foreach player.

b.) Solve the game by backwards induction. What is the SPNE of the game?

c.) Bonus: Set up the extensive form game as a normal form game (simultaneous move). Does it yield adifferent set of Nash Equilibria? If the sets are different, how does this relate to the notion of "emptythreats" and the refinement of Nash equilibria?