country (in $bn) are given in the payoff matrix below: USA Close Open Close 3, 2 12, 8 China Open 10, - 80 35, 20 a) Suppose that each nation knows the payoff matrix shown above, and believes that the other country will choose rationally (to maximise its own welfare): i. Does either country have a dominant strategy? Explain. (5 marks) ii. Is there any Nash equilibrium in this game? Explain. (2 marks) b) Now suppose that China is uncertain that the US will choose rationally. Specifically, China is concerned that President Grump and other like-minded US politicians may want to penalise China, even if it not in the US's best interest to do so. How might this concern affect China's choice of policy-strategy? How might this change the equilibrium? Explain