1 Continued Overleaf
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2 Continued Overleaf
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3 Continued Overleaf
Students must answer any TWO questions. The word limit per question is 1500 words
maximum. Anything you write once you have reached the word limit will not be marked.
1. (a) Construct a choice experiment where modal preferences over prospects
cannot have an Expected Utility representation but can be represented
using Prospect Theory following Kahneman and Tversky (1979). Explain
carefully the assumptions required to construct the choice experiment and
the underlying intuition.
[30%]
(b) Suppose decision weights have the property that for some values of 𝑝,
0 < 𝑝 < 1, 𝜋(𝑝) + 𝜋(1 − 𝑝) < 1. Construct an example to show that the
representation of preferences over gambles in prospect theory may violate
dominance.
[20%]
[Total 50%]
2. (a) There are three time periods, 𝑡 = 0,1,2. Consider the following two payoff
streams 𝐴 = (𝑥, 𝑦, 𝑧), 𝑥 ≥ 0, 𝑦 ≥ 0, 𝑧 ≥ 0 and 𝐵 = (𝑥, 𝑦, 𝑧 + ), > 0. Under
quasi-hyperbolic discounting given 0 < 𝛿 ≤ 1, 0 ≤ 𝛽 < 1 (where 𝛽 denotes
the quasi-hyperbolic discount factor (present bias) and 𝛿 denotes the
exponential discount factor) and instantaneous utility is given by 𝑣(𝑐𝑡) =
𝑎𝑐𝑡 , 𝑎 > 0. Construct an example (using actual numbers for (𝑥, 𝑦, 𝑧)) for
which preference reversal is possible?
[25%]
(b) There are three time periods, 𝑡 = 0,1,2. An individual is a hyberbolic
discounter with 0 ≤ 𝛿 ≤ 1, 0 < 𝛽 ≤ 1 and there is no commitment. The
individual has to undertake a costly action in one of the time periods 𝑡 =
0,1,2. The utility cost of the action in period 𝑡 ∈ {1,2,3} is 𝑐𝑡. For which
values of 𝛿, 𝛽, 𝑐 will a naive individual will undertake the action at 𝑡 = 2?
For which values of 𝛿, 𝛽, 𝑐 will a sophisticated individual will undertake the
action at 𝑡 = 0? Explain the intuition behind this result.
[25%]
[Total 50%]
4 Continued Overleaf
3. (a) Consider the following choice experiment:
(i) You face the prospect of loosing £800 for sure. You can limit your loss by
adopting one of the two following strategies:
Strategy 1: £300 will be saved;
Strategy 2: (1/4) probability all £800 will be saved but a (3/4) probability that
nothing will be saved.
(ii) Next, consider the following two strategies:
Strategy 3: you will loose £500 for sure;
Strategy 4: you will save £800 with a (1/4) probability but loose £800 probability
(3/4).
If an agent has preferences represented by an expected utility function, show
that if you prefer Strategy 1 to Strategy 2 you must prefer Strategy 3 to Strategy
4. If the observed median preference in (i) is Strategy 1 and the median
preference in (ii) is Strategy 4, what explanation can you provide for the
preference reversal using prospect theory?
[25%]
(b) Consider the following choice experiment:
(i) Assume you have been exposed to a disease which leads to a quick and
painless death in a week. The probability you have the disease is 0.001. What
is the maximum you are willing to pay for a cure?
(ii) Suppose volunteers are required for research into the above disease. By
volunteering, you expose yourself to a 0.001 probability of contracting the
disease. What is the minimum payment you would require to be a volunteer?
If an agent has preferences represented by an expected utility function, how do
the answers to the two questions compare? If the observed modal answer to
the first question is £100 while the modal answer to the second question is
£10,000, what explanation can you provide using prospect theory?
[25%]
[Total 50%]
5 End of Paper
4. Consider the following simultaneous move game with material payoffs as
shown below:
Grab Share
Grab
2X-C, 2X-C
4X-C,0
Share
0,4X-C
2X, 2X
where X>0, C>0.
(i) Suppose 2X
which values of X, is (Share, Share) also a fairness equilibrium? Are your
computations different from those for (i) above, and if so, why?
[30%]
[Total 50%]