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]

2.     A leading politician, Polly Lastic, has a burning desire to        reduce climate change. She is trying to develop strategies to         achieve this. Polly has heard that System 1 and System 2 thinking may play a role in determining whether she develops appropriate  strategies. Polly has learned that you have some expertise in risk  taking and decision-making and has asked you to help provide the following information:

(a) Describe the differences between System 1 and System 2 thinking, and outline the conditions under which Polly is most likely to use System 1 in her decision-making.[40 marks].

(b) Discuss the ways that a decision analysis process could   help Polly to engage System 2 thinking and explain why the            structured approach to decision making suggested by decision       analysis may be helpful to her when developing her climate change strategies. [60 marks]

3.     (a) Discuss the benefits of developing a payoff matrix when     making decisions involving risk and outline the elements of the payoff matrix which might involve subjective judgements. [30   marks]

(b) Explain how two types of ‘rule of thumb’ that individuals    often employ could bias the subjective probabilities that might be needed when making decisions involving risk.[40 marks]

(c)  Outline the steps you would take to minimize the impact of these rules of thumb on subjective probability estimates.

[30 marks]

4. RoseBlueMood (RBM) plc are exploring strategies to minimize  cyber-crime associated with its website. The Directors believe that they currently have two possible strategies to choose from, L and M. The Director responsible for examining strategy L, draws a       decision tree of the possible chance events (with associated         subjective probability estimates), subsequent strategy choices (A, B, C and D) and the consequences (in terms of percentage           reduction in cyber-crime associated with their website) which she  thinks RBM will face if strategy L is chosen. This decision tree is   shown below:

Another director, responsible for identifying strategy M, suggests    that if strategy M is adopted there is a 0.5 chance that strategy M   could be implemented without any further measures being taken, in which case he estimates it would lead to a reduction of 30% in        cyber-crime. However, he feels there is a 0.5 chance that effective

implementation of strategy M would require RBM to make a further choice between implementing prevention measures S and T. If S    were adopted, he feels that there is a 0.7 chance that this would     result in a reduction in cyber-crime of 50% and a 0.3 chance that it would lead to a reduction in cyber-crime of 20%. If measure T were adopted, he believes that it would lead to the option of either          implementing technical measures U or V. If U were implemented    the Director estimates that this will reduce cyber-crime by 40% and if V were adopted, there would be a ‘p’ chance that cyber-crime      would reduce by 80% and a ‘1-p’ chance that cyber-crime would     reduce by 10%.

(a)    In the light of the information given above, draw the

complete decision tree that RBM will need in order to make informed choices about the actions they should take to       reduce cyber-crime. (No calculation required) [20 marks]

(b)     Calculate the expected reduction in cyber-crime that would occur if strategy L were adopted. [25 marks]

(c)    What is the minimum value of probability ‘p’ in order to    make strategy M, the optimal choice for RBM. [30 marks]

(d)    Explain to RBM the limitations of choosing a strategy based on maximising the expected reduction in cyber-crime. In      addition, outline what they could do to overcome these        limitations. [25 marks]

5. A large internet trading company, Goobook, is considering its strategy in the light of new taxation laws being imposed in the   UK. The Board of Directors has asked their advisors to identify  the expected amount of tax payments that they could save by   adopting alternative strategies. The advisors indicate that          Goobook have just two strategies to choose from, S and T, and the tax savings it will enjoy will depend upon the strategy they   select and the degree of aggressive tax legislation which would be applied in the UK over the next 5 years, as follows:

Likely tax savings (£ M) over the next 5 years

Degree of aggression of tax legislation in the UK

Tax

saving

strategy

S

T

Low

150

90

Medium

70

50

High

0

10

(a)    Outline how Goobook could develop a utility curve for the

Board of Directors to help them make the decision of the best strategy to follow. [30 marks]

(b)    Draw the possible shape of the Board of Director’s utility

curve if they were risk preferring for tax savings of less than £50M, risk neutral for tax savings of between £50M and      £100M and risk averse for tax savings greater than £100M. [15 marks]

Goobook estimate that the probability of a low, medium and high degree of aggression in the tax legislation is 0.4, 0.5 and 0.1,      respectively. After extensive consultation with their advisors,       Goobook come to the view that the Board’s utility function is best defined as follows:

 = (    ℎ  5  /150).

[i.e. If tax savings over the next 5 years are 75, then Utility= 0.5]

(c)    Which tax saving strategy should Goobook adopt [30 marks]