In a distant galaxy, a war opposes the forces of the Interplanetary Federation to those of the rebels of the planet X22θ

[answerhappygod]

In a distant galaxy, a war opposes the forces of the Interplanetary Federation
to those of the rebels of the planet X22θ34β1. Suppose these rebel forces have a
probability of 0.10 to have the military logistics allowing them to strike the capital of
the Interplanetary Federation. The Secretary General of the rebel forces knows perfectly well
if he has this ability but the President of the Interplanetary Federation only knows the
probability distribution (0.10 that the rebels have this ability and 0.90 that they don't
not). The leader of the rebel armed forces presents the Secretary General with a plan to attack the
Federation forces stationed on the nearby planet. The Secretary General must decide
to either approve the attack or decide to do nothing. If he decides to do nothing, the
Secretary General of the rebel forces and the President of the Interplanetary Federation will have
both a payout of 0. If the Secretary General decides to hit the stationed forces
on the neighboring planet, the President must decide whether or not to order a military response on
X22θ34β1. If the President orders a military response on X22θ34β1 and the rebels have
the logistical ability to strike the capital of the Interplanetary Federation, the payment of the
Secretary General is 0 and that of the President is -200. If the President orders a response
military on X22θ34β1 and the rebels do not have this capability, the payment of Secretary
General is -100 and the President's is 100. If the President refuses to order a retaliatory
military on X22θ34β1, the payment of the Secretary General is 200 and that of the President
-100, and this regardless of whether the rebels have or do not have the ability to strike the
capital of the Interplanetary Federation.
a) Graphically represent the extensive form of this game. (6 points)
b) This game has a hybrid equilibrium in which, if the rebels have the logistical capacity to
strike the capital of the Interplanetary Federation, the Secretary General orders a
attack against troops stationed on the neighboring planet with probability 1 and
if he does not have this capacity, he proceeds with this attack with probability p1. President
after an attack on Interplanetary Federation troops orders a
military response on X22θ34β1 with probability p2. Find the equilibrium values ​​of
p1 and p2. (6 dots)
c) What is the probability of having an interplanetary war (i.e. that the rebels have
the logistical capability to attack the capital of the Interplanetary Federation and that the
President orders a military response on X22θ34β1)? (6 dots)