5. There are 3 poker players, A, B, and 0'. They each have reference-dependent pref- erences over money m, with a reference point of r. Letting .r = m 9", their utility functions are as follows: m if m 2 U FACE) = 23: if a: S 0 if a: 2 0 vgtr) = '/$ if m g 0 (13:5 if :1: Z 0 T10(53): (:r)'3 if :c S 0 (a) [2.5 points] graph 'vA(;r;) and v3(2:). (b) [2.5 points] For player A and player B , state whether their preferences satisfy loss aversion or diminishing sensitivity. (0) [5 points] For what values of a > 0 and 5 > 0 would player C's preferences satisfy loss aversion and diminishing sensitivity? Which parameter value captures which property? Assume that player C has linear probability weights (that is, she does not have prospect theory's non-linear probability-weighting function), then her expected utility of a fifty- fifty gamble of getting either m or m' is zuc ( m - r ) + zuc ( m' - r ) Further assume the reference point of player C is r = 0, with a = 0.5 and 6 = 0.3. For parts d, e and f, answer: (i) for which value g would player C' be indifferent between not betting and taking a fifty-fifty gamble to win $g or lose $1? (ii) Does this reflect risk- loving or risk-averse behaviour? (iii) what feature of player C's reference-dependent preferences is driving this behaviour? (d) [10 points] Player C has not won or lost anything yet. (e) [10 points] Player C' is up $10.parts (1, e and f, answer: (i) for which value 9 would player C be indifferent between not betting and taking a ftyfty gamble to Win $9 or lose $1? (ii) Does this reect risk- loving 0r riskaverse behaviour? (iii) what feature of player C's referencedependent preferences is driving this behaviour? (d) [10 points] Player C has not won or lost anything yet. (e) [10 points] Player G is up $10. (f) [10 points] Player C is down $10 (g) [5 points] Referring to parts d, e, and f, when is Player C most risk averse? Explain the intuition