Pricing and Matching with Forward-Looking Buyers and Sellers

Problem definition: We study a dynamic market over a finite horizon for a single product or service in which buyers with private valuations and sellers with private supply costs arrive following Poisson processes. A single market-making intermediary decides dynamically on the ask and bid prices that will be posted to buyers and sellers, respectively, and on the matching decisions after buyers and sellers agree to buy and sell. Buyers and sellers can wait strategically for better prices after they arrive. Academic/practical relevance: This problem is motivated by the emerging sharing economy and directly speaks to the core of operations management that is about matching supply with demand. Methodology: The dynamic, stochastic, and game-theoretic nature makes the problem intractable. We employ the mechanism-design methodology to establish a tractable upper bound on the optimal profit, which motivates a simple heuristic policy. Results: Our heuristic policy is: fixed ask and bid prices plus price adjustments as compensation for waiting costs, in conjunction with the greedy matching policy on a first-come-first-served basis. These fixed base prices balance demand and supply in expectation and can be computed efficiently. The waiting-compensated price processes are time dependent and tend to have opposite trends at the beginning and end of the horizon. Under this heuristic policy, forward looking buyers and sellers behave myopically. This policy is shown to be asymptotically optimal. Managerial implications: Our results suggest that the intermediary might not lose much optimality by maintaining stable prices unless the underlying market conditions have significantly changed, not to mention that frequent surge pricing may antagonize riders and induce riders and drivers to behave strategically in ways that are hard to account for with traditional pricing models.