Truthful multi-unit double auction with transaction costs and sellers’ changing marginal costs

It is well-known that lots of sellers offer discounts for large orders because of decreasing marginal costs and large productive capacities. Then some procurement platforms provide ways for small buyers to cooperate with their procurements and get discounts from these sellers. Moreover, these transactions will incur pair-related transaction costs. Generally, buyers values and sellers’ costs are private information. Then a critical problem faced by the platforms is to induce the buyers (sellers) to reveal their values (costs) truthfully and to match the supplies and demands efficiently. To solve this problem, we design a multi-unit double auction mechanism based on the padding method where the buyers bid their values and the sellers submit their marginal costs of different quantities, and the platform selects the winners, allocates the transactions, and sets the transaction prices for both sides. We show that the mechanism is budget-balanced, individually rational, incentive-compatible, and asymptotically efficient. For the special case with zero transaction costs, we further simplify the mechanism and get some new findings. We further conduct numerical studies to compare our mechanism with four commonly used mechanisms to demonstrate its advantages and examine the impacts of some parameters on the performance of our mechanism. Finally, we consider the cases with general marginal cost structure as well as private quantity information, respectively.