In a distant galaxy, a war is being fought between the forces of the Interplanetary Federation and the rebels from planet X22341. Let's assume that the rebel forces have a probability of of having the military logistics necessary to strike the capital of the Interplanetary Federation. The Secretary-General of the rebel forces knows perfectly well whether they have this capacity, but the President of the Interplanetary Federation only knows the probability distribution () that the rebels have this capacity and (1-`) that they do not. The leader of the rebel armed forces presents the Secretary-General with a plan of attack on the forces stationed on the neighboring planet. The cost of this operation for the Secretary-General is c. If the rebels have the military logistics to strike the capital of the Interplanetary Federation, the cost is 200. However, if they do not have it, the cost is c=cn. The Secretary-General must decide whether to approve the attack or to decide to do nothing. If he decides to do nothing, both the Secretary-General of the rebel forces and the President of the Interplanetary Federation will have a payment of 0. If the Secretary-General decides to strike the forces stationed on the neighboring planet, the President must decide whether to order a military response on X22341 or not. If the President orders a military response on X22341, the payment of the Secretary-General is 200-c and that of the President is -200 if the rebel forces have the military logistics, and 100 if they do not have it. If the President refuses to order a military response on X22341, the payment of the Secretary-General is 400-c and that of the President is -100, regardless of whether the rebels have the capacity to strike the capital of the Interplanetary Federation or not. a) Graph the extensive form of this game. b) Assume that cn=450 and `=0.8. What is the equilibrium of this game? c) What is the probability of an interplanetary war (i.e. that the rebels have the logistical capacity to attack the capital of the Interplanetary Federation and that the President orders a military response on X22341)? d) Assume that c=300 and `=0.8. What is the equilibrium of this game? e) What is the probability of an interplanetary war (i.e. that the rebels have the logistical capacity to attack the capital of the Interplanetary Federation and that the President orders a military response on X22341)? f) Assume that c=300 and `=0.1. What is the equilibrium of this game? g) What is the probability of an interplanetary war (i.e. that the rebels have the logistical capacity to attack the capital of the Interplanetary Federation and that the President orders a military response on X22341)?