Relative vices and virtues have traditionally been defined according to time-inconsistent preferences. Vice products exchange small immediate rewards (e.g., pleasure) for larger delayed costs (e.g., health), while virtue products exchange small immediate costs for larger delayed rewards. This definition can be criticized because there is evidence that small amounts of beer (or chocolate) convey a long-term health benefit, whereas large quantities impose a delayed cost. Thus, we assume that virtue products can become vice products when consumption is above a certain threshold. Survey data identifies alcoholic beer as a product that gives immediate rewards and does not impose a delayed cost. Our analysis reveals a consumption threshold that supports our assumptions.
A time-inconsistent Dynkin game: from intra-personal to inter-personal equilibria
