Inter-temporal Price Discrimination with Time Inconsistent Consumers

This paper looks at the inter-temporal price discrimination game that arises when a monopolist faces naïve-time-inconsistent consumers. En route to solving this game, we introduce two new solution concepts for dynamic games where some players are time inconsistent. The first solution concept is similar in spirit to the subgame perfect Nash equilibrium, whereas the second one relies on backwards induction. Unlike in standard finite games, these solution concepts are not equivalent, even with perfect information. We then use these solution concepts to solve the inter-temporal pricing game with time inconsistent consumers. We derive implications for monopoly profits, consumer welfare and the path of prices (Coase conjecture). We conclude that time inconsistency will reduce monopoly profits and the welfare of all consumers, except of the highest valuation ones. Moreover, with time inconsistent consumers the path of prices will approach marginal cost, but at a lower rate