Final Report Summary - DMD (Dynamic Mechanism Design: Theory and Applications)
Dynamic pricing is one of the most important areas of market design. Much of this research was conducted in operations research (OR), but economists bring new, important insights. First, economists are interested in the role of incentives, and have a good set of tools that characterize the properties of good contracts in a systematic way. Second, economists place more weight on broad qualitative insights and less on, say, numerical simulation. With this background, the central idea of my work with A. Gershkov (and with others) has been to introduce private information directly into classic OR problems studying dynamic allocation, and to systematically use the tools of mechanism design in order to characterize incentive compatible allocations and derive optimal mechanisms. We were particularly interested in understanding how the elegant dynamic policies derived in the OR literature need to be modified in order to take into account information and incentive constraints. The obtained results are important from both a theoretical and a practical perspective. We also brought together useful results in operations, economics, and applied math. For example, we used theorems concerning queuing, knapsack problems, majorization, stochastic orders, and even computer tomography, that are not known to most economists. The best way to summarize the project is to briefly review the main Chapters in our book, recently published with MIT Press:
Sequential assignment of heterogenous objects: . A seller has m objects to allocate to agents who enter the market over time. The goods are of different quality and the agents have different values. For example, a football stadium wishes to allocate different tiers of seats to customers. This chapter characterizes the efficient solution and shows how to implement this when agent's values are privately known using a dynamic Vickrey Clarke Groves mechanism.
Dynamic revenue maximization with heterogeneous objects: This chapter considers the model in the previous chapter, but characterizes the incentive compatible allocations and derives the revenue maximizing mechanism by applying a novel calculus of variation approach.
The stochastic and dynamic knapsack model. A seller has m identical objects to allocate to agents entering over time. Agents have different values and different capacity demands. For example, when people go to a football game, some wish to buy one or two tickets, while others wish to purchase tickets for a large group. When agents values are privately known, this chapter characterizes implementable allocations and the revenue-maximizing mechanism. It also studies conditions under which this solution is unaffected by agents' capacities also being private information. The information here is two-dimensional, and the analysis requires methods from stochastic orders
Learning and dynamic efficiency. This chapter returns to the heterogeneous object model of the first chapters, but supposes that the seller does not know the distribution from which agents' values are drawn. It characterizes the efficient solution and studies conditions under which this is implementable when agents privately know their values. We also provide the second best mechanism for cases when the first best is not implementable. The analysis relates to the study of efficient design with interdependent values, and heavily uses insights from majorization theory.
Long-lived agents. This chapter develops models in which agents are long-lived and strategic (i.e. can time their purchases). A seller may allocate multiple objects over time or a stream of services for which agents queue, and agents may learn about their values from new information. In particular, the designer learns about demand by observing arrivals (while agents strategize over the timing of their arrival to the market). The private information is multidimensional. A major new insight is that the revenue maximizing mechanism cannot be implemented by posted prices, contrasting most exisiting results that have been obtained for simpler frameworks.
Sequential assignment of heterogenous objects: . A seller has m objects to allocate to agents who enter the market over time. The goods are of different quality and the agents have different values. For example, a football stadium wishes to allocate different tiers of seats to customers. This chapter characterizes the efficient solution and shows how to implement this when agent's values are privately known using a dynamic Vickrey Clarke Groves mechanism.
Dynamic revenue maximization with heterogeneous objects: This chapter considers the model in the previous chapter, but characterizes the incentive compatible allocations and derives the revenue maximizing mechanism by applying a novel calculus of variation approach.
The stochastic and dynamic knapsack model. A seller has m identical objects to allocate to agents entering over time. Agents have different values and different capacity demands. For example, when people go to a football game, some wish to buy one or two tickets, while others wish to purchase tickets for a large group. When agents values are privately known, this chapter characterizes implementable allocations and the revenue-maximizing mechanism. It also studies conditions under which this solution is unaffected by agents' capacities also being private information. The information here is two-dimensional, and the analysis requires methods from stochastic orders
Learning and dynamic efficiency. This chapter returns to the heterogeneous object model of the first chapters, but supposes that the seller does not know the distribution from which agents' values are drawn. It characterizes the efficient solution and studies conditions under which this is implementable when agents privately know their values. We also provide the second best mechanism for cases when the first best is not implementable. The analysis relates to the study of efficient design with interdependent values, and heavily uses insights from majorization theory.
Long-lived agents. This chapter develops models in which agents are long-lived and strategic (i.e. can time their purchases). A seller may allocate multiple objects over time or a stream of services for which agents queue, and agents may learn about their values from new information. In particular, the designer learns about demand by observing arrivals (while agents strategize over the timing of their arrival to the market). The private information is multidimensional. A major new insight is that the revenue maximizing mechanism cannot be implemented by posted prices, contrasting most exisiting results that have been obtained for simpler frameworks.