In a distant galaxy, a war opposes the forces of the Interplanetary Federation to those of the rebels of the planetX22341 . Let's assume that these rebel forces have a probability ofl of having the military logistics 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 (that the rebels have this ability and 1lthat they do not). The leader of the rebel forces presents the Secretary-General with a plan to attack the Federation forces stationed on the neighboring planet. The cost of this operation to the Secretary-General is c. If the rebels have the Eur military logistics to strike the interplanetary Federation capital, the cost is 200. On the other hand, if they do not, the cost is c = c_n. The Secretary-General must decide whether to approve the attack or to do nothing. do nothing. If he decides to do nothing, the Secretary General of the rebel forces and the President of the Federation will both 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 onX22341 . If the President orders a military strike on X22341, the Secretary General's payment is 200-c and the President's payment is -200 if the rebel forces have the military logistics and 100 if they do not. If the President refuses to order a military response to X22341, the Secretary General's payment is 400-c and the President's is -100, regardless of what the rebels have done. this regardless of whether the rebels have or do not have the ability to strike the capital of the Interplanetary Federation.

(a) Graph the extensive form of this game. b) Assume that c_n = 450 and that l= 0:8. What is the equilibrium of this game? c) What is the probability of having an interplanetary war (i.e. that the rebels have the logistical ability to attack the capital of the interplanetary Federation and that the President orders a military response on X22341)? d) Assume that c = 300 and that l= 0:8. What is the equilibrium of this game? e) What is the probability of having an interplanetary war (i.e. that the rebels have the logistical ability to attack the capital of the Interplanetary Federation and that the President orders a military response on X22341)? f) Assume that c = 300 and that l= 0:1. What is the equilibrium of this game? g) What is the probability of having an interplanetary war (i.e. that the rebels have the logistical ability to attack the capital of the interplanetary Federation and that the President orders a military response on X22341)?