(e) Below is an Act-State matrix in which the acts are X. Y and 2. There are three possible states of the world, 81, 82 and 83 whose (strictly positive) probabilities are. respectively, p1. p2 and p3. The possible payoffs are amounts of money denoted by lower case letters x, y and 2 such that x > y > z > 0. + Explain the important differences between Regret Theory (Bell, 1982; Loomes and "" e Sugden, 1982) and Disappointment Theory (Bell, 1985; Loomes and Sugden, 1986) {:{r with reference to the interactions between payoffs that each theory allows or it? disallows. In particular. explain why Regret Theory allows violations of transitivity but " does not entail violations of Savage's sure-thing principle, whereas Disappointment, I a Theory respects transitivity but allows systematic violations of the sure-thing principle. I [14 marks] ff