Three-dimensional fast electron transport for ignition-scale inertial fusion capsules

Three-dimensional hybrid PIC simulations are presented to study electron energy transport and deposition in a full-scale fast ignition configuration. Multi-prong core heating close to ignition is found when a few GA, few PW beam is injected. Resistive beam filamentation in the corona seeds the 3D current pattern that penetrates the core. Ohmic heating is important in the low-density corona, while classical Coulomb deposition heats the core. Here highest energy densities (few Tbar at 10 keV) are observed at densities above 200 g/cc. Energy coupling to the core ranges from 20 to 30%; it is enhanced by beam collimation and decreases when raising the beam particle energy from 1.5 to 5.5 MeV.Comment: 5 pages, 5 figure

Ex-post Implementation with Interdependent Valuations

We consider a social choice setting with multidimensional signals and interdependent valuations. Such frameworks have been recently and increasingly used in order to study multi-object auctions. We obtain concise characterizations of ex-post implementable (not necessarily efficient) social choice functions in terms of affine functions that associate a weight to each agent and to each alternative. These characterizations can greatly reduce the complexity of the search for a constrained efficient (i.e., second best) mechanism in the generic cases where efficient outcomes cannot be implemented.

Mixed Bundling Auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling

Mixed Bundling Auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling.

An optimal Voting System when Voting is costly

We consider the design of an optimal voting system when voting is costly. For a private values model with two alternatives we show the optimality of a voting system that combines three elements: (i) there is an arbitrarily chosen default decision and non-participation is interpreted as a vote in favor of the default; (ii) voting is sequential; (iii) not all voters are invited to participate in the vote. We show the optimality of such a voting system by first arguing that it is first best, that is, it maximizes welfare when incentive compatibility constraints are ignored, and then showing that individual incentives and social welfare are sufficiently aligned to make the first best system incentive compatible. The analysis in this paper involves some methods that are new to the theory of mechanism design, and it is also a purpose of this paper to explore these new methods.Voting; mechanism design; committees.

Ex-post implementation with interdependent valuations

We consider a social choice setting with multidimensional signals and interdependent valuations. Such frameworks have been recently and increasingly used in order to study multi-object auctions. We obtain concise characterizations of ex-post implementable (not necessarily efficient) social choice functions in terms of affine functions that associate a weight to each agent and to each alternative. These characterizations can greatly reduce the complexity of the search for a constrained efficient (i.e., second best) mechanism in the generic cases where efficient outcomes cannot be implemented

The limits of ex post implementation

The sensitivity of Bayesian implementation to agents' beliefs about others suggests the use of more robust notions of implementation such as ex-post implementation, which requires that each agent' s strategy be optimal for every possible realization of the types of other agents. We show that the only deterministic social choice functions that are ex-post implementable in generic mechanism design frameworks with multi-dimensional signals, interdependent valuations and transferable utilities, are constant functions. In other words, deterministic ex-post implementation requires that the same alternative must be chosen irrespective of agents' signals. The proof shows that ex-post implementability of a non-trivial deterministic social choice function implies that certain rates of information substitution coincide for all agents. This condition amounts to a system of differential equations that are not satis�ed by generic valuation functions