Competing for Consumers with Self-control Problems

I examine strategic implications of competing for consumers with self-control problems. For investment goods, like health clubs, I find that the equilibrium sign-up (lump-sum) fees decrease when competition intensifies, similarly to prices in standard oligopoly models. However, the equilibrium attendance (per-unit) price increases due to firms' deteriorated ability to take advantage of the consumers' self-control problems. Moreover, firms earn less profit due to consumers' self-control problems -- the firms have a unilateral incentive to charge per-unit fees lower than the marginal cost, however they cannot make up the lost margins by increasing the lump-sum fee, due to competition. The results are reversed for leisure goods (for example, credit cards)