Consider the strategic form game depicted below. Each of two countries must simultaneously decide on a course of action. Country 1 must decide whether to keep its weapons or to destroy them. Country 2 must decide whether to spy on country 1 or not. It would be an international scandal for country 1 if country 2 could prove that country 1 was keeping its weapons. The payoff matrix is as follows. Keep Destroy Spy -1,1 0,2 Don’t spy 1, -1 0,2 a) Does either player have a weakly dominant strategy? b) Find a Nash equilibrium in which neither player employs a weakly dominant strategy Now suppose that country 1 can be one of two types: ‘aggressive’ or ‘non- aggressive’. Country 1 knows its own type. Country 2 does not know country 1’s type but believes that country 1 is aggressive with probability p > 0. The payoff matrices associated with each type are given below. Aggressive Spy Keep 10, – 9 Destroy 0,2 Don’t spy 5 , -1 0,2 Don’t spy Non-aggressive Spy Keep -1,1 Destroy 0,2 0,2 c) What action must the aggressive type of country 1 take in any Bayesian Nash equilibrium? d) Assume
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