1. The UK government is attempting to develop an important trade deal with China following BREXIT. The UK government believes that they have three potential strategies that they can adopt in these negotiations (A, B and C) and China has four potential negotiating strategies (W, X, Y and Z). As a result of these negotiations, the increase in sales by the UK to China is expected to depend upon the strategies adopted by both the UK and China, as follows: If the UK adopts strategy A the increase in sales by the UK will be 8, 8, 6 and 5 (billion $) if China adopts strategies W, X, Y and Z, respectively. If the UK adopts strategy B the increase in sales by the UK will be 4, 11, 5 and 4 (billion $) if China adopts strategies W, X, Y and Z, respectively. If the UK adopts strategy C the increase in sales by the UK will be 3, 12, 6 and 7 (billion $) if China adopts strategies W, X, Y and Z, respectively. Similarly, the increase in sales by China to the UK as a result of these negotiations is expected to depend upon the strategy adopted by both China and the UK as follows: If China adopts strategy W the increase in sales by China will be 6, 5 and 7 (billion $) if the UK adopt strategies A, B and C, respectively. If China adopts strategy X the increase in sales by China will be 9, 10 and 6 (billion $) if the UK adopts strategies A, B and C, respectively. If China adopts strategy Y the increase in sales by China will be 7, 5 and 7 (billion $) if the UK adopt strategies A, B and C, respectively. If China adopts strategy Z the increase in sales by China will be 10, 6 and 6 (billion $) if the UK adopts strategies A, B and C, respectively. (a) If both China and the UK are aware of all the information given above, and both want to maximise their sales to the other country, draw the gain matrix related to these negotiations. [15 marks] (b) Explain an appropriate method for determining the likely outcome of these negotiations and use this method to determine what strategies you think the UK and China will adopt in these negotiations. [25 marks] (c) Explain why the answer you have arrived at in (b) is a stable solution to these negotiations. [20 marks] (d) Discuss under what conditions a better solution for both China and the UK could be achieved. [30 marks] (e) Explain why a zero sum formulation of these negotiations between China and the UK may not be appropriate. [10 marks]