BACAPBoston Area Colloquium in Ancient Philosophy
BACAPBluenose Atlantic Coastal Action Program (est. 1993; Canada)
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We say that a BACAP exhibits Habit-Formation if [PSI](k) - [GAMMA](k) is increasing in k.
Proposition 8 .If a BACAP B exhibits Habit-Formation, its dual D(B) exhibits Habit-Formation.
We say that a BACAP presents Harmful Addiction if it exhibits Habit Formation and Negative Internalities.
If a BACAP presents Harmful (Beneficial) Addiction, its dual D(B) exhibits Beneficial (Harmful) Addiction.
Let [alfa]:[0, [k.sup.max]] [flecha diestra] {0,1} be a rule or strategy in a BACAP B, that is, for each state level k, a(k) prescribes an admissible action.
If a induces path A in a BACAP B, then [??] induces path [XI](A) in D(B).
The above proposition shows that, given a strategy [alfa] in a BACAP B, strategy [??] as given by expression (1) has the natural interpretation of being the strategy in -D(B) induced by applying the isomorphism [XI] to [alfa].
Consider a BACAP B = [[PSI], [GAMMA], U, [gamma], [K.sub.1]] presenting beneficial addiction and where the functional U takes the specific form
In O'Donoghue and Rabin (2002), it is shown that in a BACAP as D(B) the optimal decision rule of the agent is of the cut-off type.
In a BACAP B = [[PSI], [GAMMA], U, [gamma], [k.sub.1]] presenting beneficial addiction with [PSI] and [GAMMA] convex and intertemporal utility U given by (2), the optimal decision rule is of the cutoff type.
sophistication have been studied in O'Donoghue and Rabin (2002) and in Lopez (2006) for a BACAP presenting harmful addiction under time inconsistency as given by expression (4).
O'Donoghue and Rabin (2002) show that in a BACAP B presenting harmful addiction a naif follows a cutoff rule [[alfa].sup.n] that is, there is a critical state level [k.sup.n] such that