Time-Based Competition with Benchmark Effects

We consider a duopoly where firms compete on waiting times in the presence of an industry benchmark. The demand captured by a firm depends on the gap between the firm’s offer and the benchmark. We refer to the benchmark effect as the impact of this gap on demand. The formation of the benchmark is endogenous and depends on both firms’ choices. When the benchmark is equal to the shorter of the two offered delays, we characterize the unique Pareto Optimal Nash equilibrium. Our analysis reveals a stickiness effect by which firms equate their delays at the equilibrium when the benchmark effect is strong enough. When the benchmark corresponds to the average of the two offered delays, we show the existence of a pure Nash equilibrium. In this case, we reveal a reversal effect, by which the market leader, in terms of offered shorter delay, becomes the follower when the benchmark effect is strong enough. In both cases, we show that customers benefit when an industry benchmark exists because equilibrium waiting times are shorter. Our models also capture customers’ loss aversion, which, in our setting, states that demand is more sensitive to the gap when the delay is longer than the benchmark (loss) rather than shorter (gain). We characterize the impact of this loss aversion on the equilibrium in both settings.