On the Complexity of Dynamic Mechanism Design

We introduce a dynamic mechanism design problem in which the designer wants to offer for sale an item to an agent, and another item to the same agent at some point in the future. The agent's joint distribution of valuations for the two items is known, and the agent knows the valuation for the current item (but not for the one in the future). The designer seeks to maximize expected revenue, and the auction must be deterministic, truthful, and ex post individually rational. The optimum mechanism involves a protocol whereby the seller elicits the buyer's current valuation, and based on the bid makes two take-it-or-leave-it offers, one for now and one for the future. We show that finding the optimum deterministic mechanism in this situation - arguably the simplest meaningful dynamic mechanism design problem imaginable - is NP-hard. We also prove several positive results, among them a polynomial linear programming-based algorithm for the optimum randomized auction (even for many bidders and periods), and we show strong separations in revenue between non-adaptive, adaptive, and randomized auctions, even when the valuations in the two periods are uncorrelated. Finally, for the same problem in an environment in which contracts cannot be enforced, and thus perfection of equilibrium is necessary, we show that the optimum randomized mechanism requires multiple rounds of cheap talk-like interactions

Dynamic mechanism design

AbstractIn this paper we address the question of designing truthful mechanisms for solving optimization problems on dynamic graphs with selfish edges. More precisely, we are given a graph G of n nodes, and we assume that each edge of G is owned by a selfish agent. The strategy of an agent consists in revealing to the system–at each time instant–the cost at the actual time for using its edge. Additionally, edges can enter into and exit from G. Among the various possible assumptions which can be made to model how this edge-cost modifications take place, we focus on two settings: (i) the dynamic, in which modifications can happen at any time, and for a given optimization problem on G, the mechanism has to maintain efficiently the output specification and the payment scheme for the agents; (ii) the time-sequenced, in which modifications happens at fixed time steps, and the mechanism has to minimize an objective function which takes into consideration both the quality and the set-up cost of a new solution. In both settings, we investigate the existence of exact and approximate truthful (w.r.t. to suitable equilibrium concepts) mechanisms. In particular, for the dynamic setting, we analyze the minimum spanning tree problem, and we show that if edge costs can only decrease and each agent adopts a myopic best response strategy (i.e., its utility is only measured instantaneously), then there exists an efficient dynamic truthful (in myopic best response equilibrium) mechanism for handling a sequence of k declarations of edge-cost reductions having runtime O((h+k)logn), where h is the overall number of payment changes

Dynamic Mechanism Design

We study the optimal mechanism in a dynamic sales relationship where the buyerís arrival date is uncertain, and where his value changes stochastically over time. The buyerís arrival date is the Örst date at which contracting is feasible and is his private information. To induce immediate participation, the buyer is granted positive expected rents even if his value at arrival is the lowest possible. The buyer is punished for arriving late; i.e., he expects to earn less of the surplus. Optimal allocations for a late arriver are also further distorted below Örst-best levels. Conditions are provided under which allocations converge to the e¢ cient ones long enough after contracting, and this convergence occurs irrespective of the time the contract is initially agreed (put di§erently, the so-called "principle of vanishing distortions" introduced by Battaglini (2005) continues to apply irrespective of the buyerís arrival date)

Dynamic Mechanism Design

We study the optimal mechanism in a dynamic sales relationship where the buyerís arrival date is uncertain, and where his value changes stochastically over time. The buyerís arrival date is the Örst date at which contracting is feasible and is his private information. To induce immediate participation, the buyer is granted positive expected rents even if his value at arrival is the lowest possible. The buyer is punished for arriving late; i.e., he expects to earn less of the surplus. Optimal allocations for a late arriver are also further distorted below Örst-best levels. Conditions are provided under which allocations converge to the e¢ cient ones long enough after contracting, and this convergence occurs irrespective of the time the contract is initially agreed (put di§erently, the so-called "principle of vanishing distortions" introduced by Battaglini (2005) continues to apply irrespective of the buyerís arrival date)

Dynamic Managerial Compensation: a Mechanism Design Approach

We characterize the optimal incentive scheme for a manager who faces costly effort decisions and whose ability to generate profits for the firm varies stochastically over time. The optimal contract is obtained as the solution to a dynamic mechanism design problem with hidden actions and persistent shocks to the agent's productivity. When the agent is risk-neutral, the optimal contract can often be implemented with a simple pay package that is linear in the firm's profits. Furthermore, the power of the incentive scheme typically increases over time, thus providing a possible justification for the frequent practice of putting more stocks and options in the package of managers with a longer tenure in the firm. In contrast to other explanations proposed in the literature (e.g., declining disutility of effort or career concerns), the optimality of seniority-based reward schemes is not driven by variations in the agent's preferences or in his outside option. It results from an optimal allocation of the manager's informational rents over time. Building on the insights from the risk-neutral case, we then explore the properties of optimal incentive schemes for risk-averse managers. We find that, other things equal, risk-aversion reduces the benefit of inducing higher effort over time. Whether (risk-averse) managers with a longer tenure receive more or less high-powered incentives than younger ones then depends on the interaction between the degree of risk aversion and the dynamics of the impulse responses for the shocks to the manager's type.dynamic mechanism design; adverse selection; moral hazard; incentives; optimal pay scheme; risk-aversion; stochastic process

Infinite-Horizon Mechanism Design

These notes examine the problem of how to extend envelope theorems to infinite-horizon dynamic mechanism design settings, with an application to the design of "bandit auctions."asymmetric information, stochastic processes, incentives, mechanism design JEL Classification Numbers: D82, C73, L1.