Bandit Problems

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).One-Armed Bandit, Multi-Armed Bandit, Bayesian Learning, Experimentation, Index Policy, Matching, Experience Goods

Imitation and Experimentation in a Changing Environment

This paper analyzes the equilibrium play in a random matching model with a changing environment. Under myopic decision making, players adopt imitation strategies similar to those observed in evolutionary models with sampling from past play in the population. If the players are patient, equilibrium strategies display elements of experimentation in addition to imitation. If the changes in the environment are infrequent enough, these strategies succeed in coordinating almost all of the players on the dominant action almost all of the time. The myopic rules, on the other hand, result in mis-coordination for a positive fraction of time.

Dynamic Price Competition

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.Dynamic competition, Marginal contribution, Markov perfect equilibrium, Common agency

Information in Mechanism Design

We survey the recent literature on the role of information in mechanism design. First, we discuss an emerging literature on the role of endogenous payoff and strategic information for the design and the efficiency of the mechanism. We specifically consider information management in the form of acquisition of new information or disclosure of existing information. Second, we argue that in the presence of endogenous information, the robustness of the mechanism to the type space and higher order beliefs becomes a natural desideratum. We discuss recent approaches to robust mechanism design and robust implementation.Mechanism Design, Information Acquisition, Ex Post Equilibrium, Robust Mechanism Design, Interdependent Values, Information Management

The Dynamic Pivot Mechanism

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. We show that the dynamic pivot mechanism is equivalent to a modified second price auction.Pivot mechanisms, Dynamic mechanism design, Ex-post equilibrium, Marginal contribution, Multi-armed bandit, Bayesian learning

Entry and Innovation in Vertically Differentiated Markets

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.Experience goods, vertical differentiation, entry, innovation

Information in Mechanism Design

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.Mechanism Design, Information Acquisition, Ex Post Equilibrium, Robust Mechanism Design, Interdependent Values, Information Management

Entry and Vertical Differentiation

This paper analyzes the entry of new products into vertically differentiated markets where an entrant and an incumbent compete in quantities. The value of the new product is initially uncertain and new information is generated through purchases in the market. We derive the (unique) Markov perfect equilibrium of the infinite horizon game under the strong long run average payoff criterion. The qualitative features of the optimal entry strategy are shown to depend exclusively on the relative ranking of established and new products based on current beliefs. Superior products are launched relatively slowly and at high initial prices whereas substitutes for existing products are launched aggressively at low initial prices. The robustness of these results with respect to different model specifications is discussed. Classification-JEL: C72, C73, D43, D83 Keywords: Entry, Duopoly, Quantity Competition, Vertical Differentiation, Bayesian Learning,Markov Perfect Equilibrium, Experimentation, Experience Goods

Entry and Vertical Differentiation

This paper analyzes the entry of new products into vertically differentiated markets where an entrant and an incumbent compete in quantities. The value of the new product is initially uncertain and new information is generated through purchases in the market. We derive the (unique) Markov perfect equilibrium of the infinite horizon game under the strong long run average payoff criterion. The qualitative features of the optimal entry strategy are shown to depend exclusively on the relative ranking of established and new products based on current beliefs. Superior products are launched relatively slowly and at high initial prices whereas substitutes for existing products are launched aggressively at low initial prices. The robustness of these results with respect to different model specifications is discussed.Entry, Duopoly, Quantity Competition, Vertical Differentiation, Bayesian Learning, Markov Perfect Equilibrium, Experimentation, Experience Goods

Monopoly Pricing of Experience Goods

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.Monopoly, dynamic pricing, learning, experience goods, continuous time, Markov perfect equilibrium