Dynamic pricing with multiple consumers and alternating offers under retailer competition: theory and experiment

We introduce and test a stylized model of dynamic pricing under duopolistic competition. In our model, a consumer receives alternating price offers between two retailers over an indefinite number of periods so that the game or “season” terminates with a fixed probability after each period. The two retailers do not know the valuation of the consumer for the good they are competing to sell to the consumer, but they have common knowledge about the probability distribution of the valuation. Our equilibrium analysis suggests that price offers decrease exponentially across periods over the season. Moreover, when there are multiple consumers in the game, as long as their valuations are ex ante independently and identically distributed, the equilibrium predictions are the same regardless of the number of consumers. An experiment on the model showed that subjects acting as retailers often overpriced relative to equilibrium predictions. In addition, the theoretical invariance with respect to the number of consumers did not hold: consumers seemed to be more prone to strategic waiting in the first period of the season when there were multiple consumers (compared with when there was only a single consumer), leading to a decrease in the per-consumer payoff of the retailer who made the price offer in the first period and a corresponding increase in per-consumer payoff of the other retailer. There is also evidence of within-session evolution that led to lower retailer prices that were closer to equilibrium predictions, and higher tendency for consumer strategic waiting, as the session progressed.