MANG6134W1

SEMESTER 2 EXAMINATIONS 2018-19

RISK TAKING AND DECISION MAKING

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 ifV 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:

(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:

utility = (Likely tax savings oveT tℎe next 5 yeaTs /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]

(d)    Explain to Goobook what prospect theory suggests is the likely shape of their probability weighting function and how  this might influence the decision arrived at in (c). [25 marks]

6.     A leading international charity, Bringhope, is exploring means of reducing famine and hardship in Yemen, because of the recent war. They have developed a number of alternative approaches they could adopt and the likely outcomes (in terms of reductions in famine and hardship) which would result from a combination of the approach they adopt and the continuing level of violence in the country.

(a)    Explain to Bringhope the value of quantifying probability judgements in this situation and explain why subjective, rather than objective, probabilities are likely to be of most value to them.                    [30 marks]

(b)  Outline a systematic approach to probability assessment using multiple probability assessors that could be used by Bringhope. Discuss how this approach could help to improve the accuracy of the estimated probabilities.          [40 marks]

(c)  Describe a technique that could be employed by Bringhope to assess the probability of events that only have a very small  probability of occurring.               [25 marks]