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 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. I also show that for plausible parameter regions the market adjusts to consumers' self‐control problem in such a way that firms play the standard equilibrium strategies that they would have engaged in with fully rational consumers, with identical market outcomes. Most of the results are qualitatively the same for leisure goods (for example, credit cards); however, some results are reversed: the per‐unit fees are higher than marginal cost and decrease as competition intensifies.