Economics In the attic of their home. siblings As] and Rose have used their illusion to create a lovely paradise city with their Loco\". Yet. Aid is known for not hauinl a lot of patience. In the evening he considers whether he should go to the attic and Destroy the city or to Keep it. Rose is aware ofthis potential threat and must decide whether to spy on As! or not. It would be bad for Aid if his sister could see that he was trying to destroy their joint work because she linit'iulid then inform the parents. The payoff matrix is as follows: a [4] Does either Ax! or Rose have a weakly dominant strategy? Find the pure strata\" Nash equilibria of this game. if any. Neat suppose that Fuel can be one of two types: 'aggresiue' or 'non-aggresiue'. Aid knows which type he is Rose does not know Axl's type. but believes that he is anteahie with probability p. The aggressive utl nds it of utmost importance to destroy the city. If he does so and finds Rose spyin; on him:1 he will punch her hard on her nose [M will justify this action to the parents by pointing to Rose's spying on him]. When M is of the non-aggressive type. the payoffs are as before. The payoff matricu associated with each poible type of Anti are as follows: If Aid is of the antessiue type {with probability p]: b [3] Which action must the aggressive nd tales in any Bayesian-Nash equilibrium? c [E] For which values of ,1! does this game have a Bayesian-Nash equilibrium in pure strategies? Is it unique? d [1"] Suppose that House plays Spy with probability o and that the non-aggresiue Attl plays Destroy with probability a :a- I}. Find a Bayesian-Hath equilibrium in completely nth-red strategies