Nash implementation with little communication

The paper considers the communication complexity (measured in bits or real numbers) of Nash implementation of social choice rules. A key distinction is whether we restrict to the traditional one-stage mechanisms or allow multi-stage mechanisms. For one-stage mechanisms, the paper shows that for a large and important subclass of monotonic choice rules -- called "intersection monotonic" -- the total message space size needed for one-stage Nash implementation is essentially the same as that needed for "verification" (with honest agents who are privately informed about their preferences). According to Segal (2007), the latter is the size of the space of minimally informative budget equilibria verifying the choice rule. However, multi-stage mechanisms allow a drastic reduction in communication complexity. Namely, for an important subclass of intersection-monotonic choice rules (which includes rules based on coalitional blocking such as exact or approximate Pareto efficiency, stability, and envy-free allocations) we propose a two-stage Nash implementation mechanism in which each agent announces no more than two alternatives plus one bit per agent in any play. Such two-stage mechanisms bring about an exponential reduction in the communication complexity of Nash implementation for discrete communication measured in bits, or a reduction from infinite- to low-dimensional continuous communication.Monotonic social choice rules, Nash implementation, communication complexity,verification, realization, budget sets, price equilibria

What Makes them Click: Empirical Analysis of Consumer Demand for Search Advertising

We study users' response to sponsored-search advertising using data from Microsoft's Live AdCenter distributed in the "Beyond Search" initiative. We estimate a structural model of utility maximizing users, which quantifies "user experience" based on their "revealed preferences," and predicts user responses to counterfactual ad placements. In the model, each user chooses clicks sequentially to maximize his expected utility under incomplete information about the relevance of ads. We estimate the substitutability of ads in users' utility function, the fixed effects of different ads and positions, user uncertainty about ads' relevance, and user heterogeneity. We find substantial substitutability of ads, which generates large negative externalities: 40% more clicks would occur in a hypothetical world in which each ad faces no competition. As for counterfactual ad placements, our simulations indicate that CTR-optimal matching increases CTR by 10.1% while user-optimal matching increases user welfare by 13.3%. Moreover, targeting ad placement to specific users could raise user welfare by 59%. Here, we find a significant suboptimality (up to 16% of total welfare) in case the search engine tries to implement a sophisticated matching policy using a misspecified model that does not account for externalities. Finally, user welfare could be raised by 14% if they had full information about the relevance of ads to them.

Antitrust in Innovative Industries

We study the effects of antitrust policy in industries with continual innovation. A more protective antitrust policy may have conflicting effects on innovation incentives, raising the profits of new entrants, but lowering those of continuing incumbents. We show that the direction of the net effect can be determined by analyzing shifts in innovation benefit and supply holding the innovation rate fixed. We apply this framework to analyze several specific antitrust policies. We show that in some cases, holding the innovation rate fixed, as suggested by our comparative statics results, the tension does not arise and a more protective policy necessarily raises the rate of innovation.

A simple status quo that ensures participation (with application to efficient bargaining)

We consider Bayesian incentive-compatible mechanisms with independent types and either private values or interdependent values that satisfy a form of "congruence." We show that in these settings, interim participation constraints are satisfied when the status quo is the randomized allocation that has the same distribution as the equilibrium allocation in the mechanism. Moreover, when utilities are convex in the allocation, we can instead satisfy participation constraints with the deterministic status quo equal to the expected equilibrium allocation in the mechanism. For quasilinear settings, these observations imply the possibility of efficient bargaining when the status quo specifies the expected efficient decision provided that the total surplus is convex in the decision.Efficient property rights, asymmetric information bargaining, transaction costs

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.

Dynamic Mechanism Design: Incentive Compatibility, Profit Maximization and Information Disclosure

This paper examines the problem of how to design incentive-compatible mechanisms in environments in which the agents' private information evolves stochastically over time and in which decisions have to be made in each period. The environments we consider are fairly general in that the agents' types are allowed to evolve in a non-Markov way, decisions are allowed to affect the type distributions and payoffs are not restricted to be separable over time. Our first result is the characterization of a dynamic payoff formula that describes the evolution of the agents' equilibrium payoffs in an incentive-compatible mechanism. The formula summarizes all local first-order conditions taking into account how current information affects the dynamics of expected payoffs. The formula generalizes the familiar envelope condition from static mechanism design: the key difference is that a variation in the current types now impacts payoffs in all subsequent periods both directly and through the effect on the distributions of future types. First, we identify assumptions on the primitive environment that guarantee that our dynamic payoff formula is a necessary condition for incentive compatibility. Next, we specialize this formula to quasi-linear environments and show how it permits one to establish a dynamic "revenue-equivalence" result and to construct a formula for dynamic virtual surplus which is instrumental for the design of optimal mechanisms. We then turn to the characterization of sufficient conditions for incentive compatibility. Lastly, we show how our results can be put to work in a variety of applications that include the design of profit-maximizing dynamic auctions with AR(k) values and the provision of experience goods.dynamic mechanisms, asymmetric information, stochastic processes, incentives

The Communication Requirements of of Social Choice Rules and Supporting Budget Sets

The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any communication verifying that an alternative is in the rule must reveal supporting budget sets for the agents such that the optimality of the proposed alternative to all agents within their respective budget set in itself verifies the alternative. We characterize the budget equilibria that are the minimally informative messages verifying a given choice rule. This characterization is used to identify the communication burden of choice rules, measured with the number of transmitted bits or real variables. Applications include efficiency in convex economies, exact or approximate surplus maximization in combinatorial auctions, the core in indivisible good economies, and stable many-to-one matchings.social choice rules, budget equilibria, choice rules efficiency in convex economies