Delayed discounting (DD) is a behavioral index of impulsive decision-making, defined as a preference of smaller, sooner rewards to a larger, later reward as time passes \citep{Loewenstein_1992,Raineri_1993} . DD was widely used by behavioral economists and social and clinical psychologists in the assessment of individuals’ preference for future versus immediate outcomes. The degree to which an individual subjectively devalue future rewards was captured by a hyperbolic function, where steeper curvature reflect greater discounting of delayed rewards \citep{McKerchar2009,Yi2009,Myerson_2001,Myerson_1995,Green_1994,Rachlin_1972}. High rates of delay discounting were found associated with a wide range of impulsive behaviors, including abusive use of substance  \cite{Wilson2015,Sheffer2012} , pathological gambling \cite{Alessi_2003} , overeating \cite{Reimers_2009,Price_2014}impulsive consumption (\cite{Dittmar_2010,Chen_2005}).  With its intertemporal nature,  substantial theoretical and empirical studies have indicated that DD linked to future behavior prediction.   
Studies found that DD was a strong prognostic indicator of smoking relapse.