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To expand on @1muflon1's answer. The theory of rational addiction assumes that the utility of a consumer at time instance $t$ depends both on current consumption of the addicitve good, say $c_t$, and the consumption of the addictive good in the past. For simplicity say $c_{t-1}$. So at period $t$ the instantaneous utility looks something like:  u(c_t, c_{t-...
It is possible for an addict to be rational. A famous work on this was done by Becker (1988) Theory of Rational addiction. In order for agent to have rational preferences the preferences have to satisfy the following definition (See MWG Microeconomic Theory pp 6): Definition 1.B.1: The preference relation $\succeq$ is rational if it possesses the following ...