Submodularity if a a u b then a u c a u b u c for all

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Submodularity : If A ~ A U B then A U C ~ A U B U C for all menus C Preferences satisfy completeness, transitivity, monotonicity and submodularity if and only if there are u 1 ….. u n such that U(A) = max x in A u 1 (x) + max x in A u 2 (x) …. + max x in A u n (x) is a utility representation. preference for commitment means that a smaller menu A is chosen over a larger one B. For example, {x} > {x, y}. This behavior can describe an agent who keeps only healthy foods and drinks at home,
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requests self-exclusions from casino gambling, uses the StayFocused application to limit Internet surfing, • Multi-self model of commitment. (Strotz, 55) Model of costly self-control . (Gul, Pesendorfer 01). Both approaches distinguish two different utility functions: u is the normative utility that describes long-term values v is the temptation utility that describes spontaneous temptations Marketing policies: Investment goods (immediate costs, delayed rewards) – front loaded contracts. Example: health clubs. Pleasure goods (immediate rewards, delayed costs) – back loaded contracts . Example: credit cards. Governments often want to impose some agenda on their citizens. The government policies may include Prohibition Taxation Education •Nudges (Thaler-Sunstein’s book) – policies that are (i) cheap to implement, (ii) alter people’s behavior in a predictable way and (iii) do not significantly change their available options and economic incentives. (ex. Defaults in organ donation to incr. Compliance rates)(ex. Prepayment of taxes; most employees get an annual tax refund) Firms cannot use prohibition or taxation. Education is advertising . Nudges are marketing tricks. Fudenberg and Levine (06): dual-self model favors taxation . Gul and Pesendorfer (07): costly self-control favors prohibition . Why the difference? Dual-self model implies indifference {x, y} ~ {x} > {y} when x is chosen in {x, y} and y is resisted. Costly self-control model implies a preference for commitment {x} > {x, y} even if x is chosen in {x, y} but y is tempting. Therefore having temptations around can impose cognitive costs even on people who can resist them.
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