Question
In a distant galaxy, a war opposes the forces of the Interplanetary Federation to those of the rebels of the planet X22034. Suppose that these
In a distant galaxy, a war opposes the forces of the Interplanetary Federation to those of the rebels of the planet X22034. Suppose that these rebel forces have a probability of l to have 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 capacity but the President of the Interplanetary Federation only knows the probability distribution (1 that the rebels have this capacity and 1-l that they do not have it). The leader of the rebel armed forces presents the Secretary General with a plan to attack the Federation forces stationed on the neighboring planet. The cost of this operation for the Secretary General is c. If the rebels have the military logistics allowing them to strike the capital of the Interplanetary Federation, this cost is 200. On the other hand, if they do not have them, this cost is c = C. 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 both have a payout of 0. If the Secretary General decides to strike the forces stationed on the neighboring planet, the President must decide whether or not to order a military response on X2203431. If the President orders a military response on X220341, the General Secretary's payout is 200 -c and the President's payout 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 X22034B1, the General Secretary's payout is 400 - c and the President's payout is - 100, regardless of whether the Rebels have or have no ability to strike the Interplanetary Federation capital.
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