We study dynamic mechanisms for optimizing revenue in repeated auctions, that are robust to heterogeneous forward-looking and learning behavior of the buyers. Typically it is assumed that the buyers are either all myopic or are all infinite lookahead, and that buyers understand and trust the mechanism. These assumptions raise the following question: is it possible to design approximately revenue optimal mechanisms when the buyer pool is heterogeneous? Facing a heterogeneous population of buyers with an unknown mixture of @math -lookahead buyers, myopic buyers, no-regret-learners and no-policy-regret learners, we design a simple state-based mechanism that achieves a constant fraction of the optimal achievable revenue.
We consider a pricing problem where a buyer is interested in purchasing using a good, such as an app or music or software, repeatedly over time. The consumer discovers his value for the good only as he uses it, and the value evolves with each use. Optimizing for the seller's revenue in such dynamic settings is a complex problem and requires assumptions about how the buyer behaves before learning his future value(s), and in particular, how he reacts to risk. We explore the performance of a class of pricing mechanisms that are extremely simple for both the buyer and the seller to use: the buyer reacts to prices myopically without worrying about how his value evolves in the future; the seller needs to optimize for revenue over a space of only two parameters, and can do so without knowing the buyer's risk profile or fine details of the value evolution process. We present simple-versus-optimal type results, namely that under certain assumptions, simple pricing mechanisms of the above form are approximately optimal regardless of the buyer's risk profile. Our results assume that the buyer's value per usage evolves as a martingale. For our main result, we consider pricing mechanisms in which the seller offers the product for free for a certain number of uses, and then charges an appropriate fixed price per usage. We assume that the buyer responds by buying the product for as long as his value exceeds the fixed price. Importantly, the buyer does not need to know anything about how his future value will evolve, only how much he wants to use the product right now. Regardless of the buyers' initial value, our pricing captures as revenue a constant fraction of the total value that the buyers accumulate in expectation over time. We characterize the profit-maximizing mechanism for repeatedly selling a non-durable good in continuous time. The valuation of each agent is private information and changes over time. At the time of contracting every agent privately observes his initial type which influences the evolution of his valuation process. In the profit-maximizing mechanism the allocation is distorted in favor of agents with high initial types. We derive the optimal mechanism in closed form, which enables us to compare the distortion in various examples. The case where the valuation of the agents follows an arithmetic geometric Brownian motion, Ornstein-Uhlenbeck process, or is derived from a Bayesian learning model are discussed. We show that depending on the nature of the private information and the valuation process the distortion might increase or decrease over time. Abstract Regulation typically involves a continuing relationship between a regulator and a firm, and that relationship is often complicated by asymmetric information. A multiperiod model of this relationship is analyzed in which a regulated firm has private information about its costs which may changed over time in a manner observable only to the firm. The regulator is assumed to be able to commit to a policy for the entire regulatory horizon, and the optimal pricing policy is shown to depend on an informativeness measure that indicates how information by the firm in one period will be used in future periods. We consider the problem of designing optimal mechanisms for settings where agents have dynamic private information. We present the virtual-pivot mechanism, which is optimal in a large class of environments that satisfy a separability condition. The mechanism satisfies a rather strong equilibrium notion (it is periodic ex post incentive compatible and individually rational). We provide both necessary and sufficient conditions for immediate incentive compatibility for mechanisms that satisfy periodic ex post incentive compatibility in future periods. The result also yields a strikingly simple mechanism for selling a sequence of items to a single buyer. We also show that the allocation rule of the virtual-pivot mechanism has a very simple structure (a virtual index) in multiarmed bandit settings. Finally, we show through examples that the relaxation technique we use does not produce optimal dynamic mechanisms in general nonseparable environments.  Abstract Multi-period contracts with adverse selection at the time of contracting are studied. With risk-neutrality and independent private information, all inefficiency arises in the first period only. With positive serial correlation, inefficiency is more pervasive but declines over time. This paper constructs an efficient, budget-balanced, Bayesian incentive-compatible mechanism for a general dynamic environment with quasilinear payoffs in which agents observe private information and decisions are made over countably many periods. First, under the assumption of "private values" (other agents' private information does not directly affect an agent's payoffs), we construct an efficient, ex post incentive-compatible mechanism, which is not budget-balanced. Second, under the assumption of "independent types" (the distribution of each agent's private information is not directly affected by other agents' private information), we show how the budget can be balanced without compromising agents' incentives. Finally, we show that the mechanism can be made self-enforcing when agents are sufficiently patient and the induced stochastic process over types is an ergodic finite Markov chain. [PUBLICATION ABSTRACT] We study mechanism design in dynamic quasilinear environments where private information arrives over time and decisions are made over multiple periods. We make three contributions. First, we provide a necessary condition for incentive compatibility that takes the form of an envelope formula for the derivative of an agent's equilibrium expected payoff with respect to his current type. It combines the familiar marginal effect of types on payoffs with novel marginal effects of the current type on future ones that are captured by “impulse response functions.” The formula yields an expression for dynamic virtual surplus that is instrumental to the design of optimal mechanisms and to the study of distortions under such mechanisms. Second, we characterize the transfers that satisfy the envelope formula and establish a sense in which they are pinned down by the allocation rule (“revenue equivalence”). Third, we characterize perfect Bayesian equilibrium‐implementable allocation rules in Markov environments, which yields tractable sufficient conditions that facilitate novel applications. We illustrate the results by applying them to the design of optimal mechanisms for the sale of experience goods (“bandit auctions”).  