We provide an introduction into the recent developments of dynamic mechanism design with a primary focus on the quasilinear case. First, we describe socially optimal (or efficient) dynamic mechanisms. These mechanisms extend the well known Vickrey-Clark-Groves and D’Aspremont-Gérard-Varet mechanisms to a dynamic environment. Second, we discuss results on revenue optimal mechanism. We cover models of sequential screening and revenue maximizing auctions with dynamically changing bidder types. We also discuss models of information management where the mechanism designer can control (at least partially) the stochastic process governing the agent’s types. Third, we consider models with changing populations of agents over time. This allows us to address new issues relating to the properties of payment rules. After discussing related models with risk-averse agents, limited liability, and different performance criteria for the mechanisms, we conclude by discussing a number of open questions and challenges that remain for the theory of dynamic mechanism design.
This note constructs an efficient mechanism for finding the best candidate for a committee from a sequence of potential candidates. Committee members have independent private values information about the quality of the candidate. The mechanism selects the best candidate according to the standard utilitarian welfare criterion. Furthermore, the mechanism can be modified to have a balanced budget.
We consider truthful implementation of the socially efficient allocation in an independent private-value environment in which agents receive private information over time. We propose a suitable generalization of the pivot mechanism, based on the marginal contribution of each agent. In the dynamic pivot mechanism, the ex-post incentive and ex-post participation constraints are satisfied for all agents after all histories. In an environment with diverse preferences it is the unique mechanism satisfying ex-post incentive, ex-post participation and efficient exit conditions.
We develop the dynamic pivot mechanism in detail for a repeated auction of a single object in which each bidder learns over time her true valuation of the object. The dynamic pivot mechanism here is equivalent to a modified second price auction.
We consider an auction environment with interdependent values. Each bidder can learn her payoff type through costly information acquisition. We contrast the socially optimal decision to acquire information with the equilibrium solution in which each agent has to privately bear the cost of information acquisition.
In the context of the generalized Vickrey-Clarke-Groves mechanism, we establish that the equilibrium level exceeds the socially optimal level of information with positive interdependence. The individual decisions to acquire information are strategic substitutes. The difference between the equilibrium and the efficient level of information acquisition is increasing in the interdependence of the bidders’ valuations and decreasing in the number of informed bidders.
JEL Classification: C72, C73, D43, D83
Keywords: Vickrey-Clarke-Groves mechanism, Information acquisition, Strategic substitutes, Informational efficiency
We consider truthful implementation of the socially efficient allocation in a dynamic private value environment in which agents receive private information over time. We propose a suitable generalization of the Vickrey-Clarke-Groves mechanism, based on the marginal contribution of each agent. In the marginal contribution mechanism, the ex post incentive and ex post participations constraints are satisfied for all agents after all histories. It is the unique mechanism satisfying ex post incentive, ex post participation and efficient exit conditions.
We develop the marginal contribution mechanism in detail for a sequential auction of a single object in which each bidders learn over time her true valuation of the object. We show that a modified second price auction leads to truthtelling.
Keywords: Vickrey-Clarke-Groves mechanism, Pivot mechanism, Ex post equilibrium, Marginal contribution, Multi-armed bandit, Bayesian learning
We consider the truthful implementation of the socially efficient allocation in a dynamic private value environment in which agents receive private information over time. We show that a suitable generalization of the Vickrey-Clark-Groves mechanism, based on the marginal contribution of each agent, leads to truthtelling in every period.
A leading example of a dynamic allocation model is the sequential auction of a single good in which the current winner of the object receives additional information about her valuation. We show that a modified sequential second price auction in which only the current winner makes a positive payment leads to truthtelling. In general allocation problems, the marginal contribution mechanism continues to induce truthtelling in every period but may now include positive transfers for many agents.
We survey the literature on multi-armed bandit models and their applications in economics. The multi-armed bandit problem is a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. This classic problem has received much attention in economics as it concisely models the trade-off between exploration (trying out each arm to find the best one) and exploitation (playing the arm believed to give the best payoff).
We survey the recent literature on the role of information for mechanism design. We specifically consider the role of endogeneity of and robustness to private information in mechanism design.
We view information acquisition of and robustness to private information as two distinct but related aspects of information management important in many design settings. We review the existing literature and point out directions for additional future work.
Keywords: Mechanism Design, Information Acquisition, Ex Post Equilibrium, Robust Mechanism Design, Interdependent Values, Information Management
We develop a dynamic model of experience goods pricing with independent private valuations. We show that the optimal paths of sales and prices can be described in terms of a simple dichotomy. In a mass market, prices are declining over time. In a niche market, the optimal prices are initially low followed by higher prices that extract surplus from the buyers with a high willingness to pay. We consider extensions of the model to integrate elements of social rather than private learning and turnover among buyers.
We consider the model of price competition for a single buyer among many sellers in a dynamic environment. The surplus from each trade is allowed to depend on the path of previous purchases, and as a result, the model captures phenomena such as learning by doing and habit formation in consumption characterize Markovian equilibria for finite and infinite horizon versions of the model and show that the stationary infinite horizon version of the model possesses an equilibrium where all the sellers receive an equilibrium payoff equal to their marginal contribution to the social welfare.
Keywords: Dynamic competition, Marginal contribution, Markov perfect equilibrium, Common agency
A model of repeated price competition with large buyers is analyzed. The sellers are allowed to offer different prices to different buyers and the buyers act strategically. The set of subgame perfect Equilibria is investigated under public and private monitoring.
With public monitoring the equilibrium set with large buyers expands relative to the standard model where each buyer is small and behaves myopically.
With private monitoring, where prices are not observable to the competing sellers, the set of equilibrium payoffs shrinks. In the finitely repeated game with private monitoring, all sales are made by the efficient seller. In the infinitely repeated game this result is preserved as long as the sellers condition their prices on the public history. In contrast to the finite horizon game, the set of pure strategy equilibria expands if the sellers are allowed to condition their own past prices. Comparisons are drawn to Markovian equilibria of similar dynamic games.
This note shows that the optimal choice of k simultaneous experiments in a stationary multi-armed bandit problem can be characterized in terms of the Gittins index of each arm. The index characterization remains equally valid after the introduction of switching costs.
This paper analyzes the optimal entry into experience goods markets with vertically differentiated buyers. We consider the case where the value of the new product is imperfectly known, but common to all buyers (common values) as well as the case where the quality is different across buyers (private values).
We distinguish between new products that are improvements to existing products and new products that are substitutes. Different types of products have qualitatively distinct diffusion paths. Improvements are introduced slowly relative to the full information case, while substitutes are introduced more aggressively. The slow entry strategy is associated with increasing supply and decreasing prices over time. The reverse pattern holds for an aggressive entry strategy
The incentives to innovate display a similar distinction. A firm with a currently inferior product opts for a large but risky innovation, whereas a currently superior producer chooses a smaller but certain innovation.