On Local and Network Games

The knowledge constraints and transactions costs imposed by geographical distance, network connections and time conspire to justify local behavior as a good approximation for global rationality. We consider a class of games to illustrate this relationship and raise some questions as to what constitutes a satisfactory solution concept.Local games, Network games, Advertising

Absenteeism, Substitutes, and Complements in Simple Games

A voting with absenteeism game is defined as a pair (G;r) where G is an n-player (monotonic) simple game and r is an n-vector for which r_i is the probability that player i attends a vote. We define a power index for such games, called the absentee index. We axiomatize the absentee index and provide a multilinear extension formula for it. Using this analysis we re-derive Myerson's (1977, 1980) ibalanced contributionsi property for the Shapley-Shubik power index. In fact, we derive a formula which quantitatively gives the amount of the ibalanced contributionsi in terms of the coefficients of the multilinear extension of the game. Finally, we define the notion of substitutes and complements in simple games. We compare these concepts with the familiar concepts of dummy player, veto player, and master player.Simple game, Shapley-Shubik power index, Absenteeism, Multilinear extension, Balanced contributions, Substitute, Complement

Ambrose Burnside, the Ninth Army Corps, and the Battle of Spotsylvania Court House

The fighting on May 12, 1864 at Spotsylvania Court House evokes thoughts of the furious combat at the Bloody Angle. However, there is another aspect of the fighting on May 12, that is, incidentally, at another salient. The then-independent command of Ambrose Burnside’s Ninth Corps spent the day fighting on the east flank of the Mule Shoe, and charging against the Confederate right flank at Heth’s Salient. This paper has two parts: the first half analyzes the complexities and problems of Burnside’s return to the Eastern Theater since his disastrous defeat at Fredericksburg in 1862, starting in April 1864 and culminating with the opening moves of the Overland Campaign. In the second half the paper examines the fighting on May 12—tactically how and why Burnside was repulsed, while strategically it examines the larger repercussions of the fighting on May 12, including the pivotal position of Heth’s Salient in defending Lee’s flank and reserve line. I would like to acknowledge the staff and volunteers at the Fredericksburg and Spotsylvania National Military Park for their help with this paper. Especial thanks are due to Peter Maugle, Eric Mink and Rebecca Capobianco for their assistance in a last-minute request locating Henry Heth’s official report

Self-Energy Correction to the Bound-Electron g Factor of P States

The radiative self-energy correction to the bound-electron g factor of 2P_1/2 and 2P_3/2 states in one-electron ions is evaluated to order alpha (Z alpha)^2. The contribution of high-energy virtual photons is treated by means of an effective Dirac equation, and the result is verified by an approach based on long-wavelength quantum electrodynamics. The contribution of low-energy virtual photons is calculated both in the velocity and in the length gauge and gauge invariance is verified explicitly. The results compare favorably to recently available numerical data for hydrogenlike systems with low nuclear charge numbers.Comment: 8 pages, RevTe

Absenteeism, Substitutes, and Complements and the Banzhaf Index

We consider the voting-with-absenteeism game of Quint-Shubik (2003). In that paper we defined a power index for such games, called the absentee index. Our analysis was based on the theory of the Shapley-Shubik power index (SSPI) for simple games. In this paper we do an analogous analysis, based on the Banzhaf index instead of the SSPI. The result is a new index, called the absentee Banzhaf index. We provide an axiomatization and multilinear extension formula for this index. Finally, we re-explore Myerson's (1977, 1980) "balanced contributions" property, and the concept of substitutes and complements for simple games (Quint-Shubik 2003), again basing our analysis on the Banzhaf index instead of the SSPI.Simple game, Shapley-Shubik power index, Banzhaf index, Absenteeism, Multilinear extension, Balanced contributions, Substitute, Complement

Relationships, Rigor, and Readiness: Strategies for Improving High Schools

This report offers lessons from the last in a series of three high school reform conferences sponsored by MDRC, the Council of the Great City Schools, and the National High School Alliance. This conference in June 2007 brought together leaders from 22 midsize school districts to describe their reform initiatives and to discuss ways in which research and evaluation can inform and complement school change

Anglo-Dutch premium auctions in eighteenth-century Amsterdam

An Anglo-Dutch premium auction consists of an English auction followed by a Dutch auction, with a cash premium paid to the winner of the first round. We study such auctions used in the secondary debt market in eighteenth-century Amsterdam. This was among the first uses of auctions, or any structured market-clearing mechanism, in a financial market. We find that this market presented two distinct challenges - generating competition and aggregating information. We argue that the Anglo-Dutch premium auction is particularly well-suited to do both. Modeling equilibrium play theoretically, we predict a positive relationship between the uncertainty in a security's value and the likelihood of a second-round bid. Analyzing data on 16,854 securities sold in the late 1700s, we find empirical support for this prediction. This suggests that bidding behavior may have been consistent with (non-cooperative) equilibrium play, and therefore that these auctions were successful at generating competition. We also find evidence suggesting that these auctions succeeded at aggregating information. Thus, the Anglo-Dutch premium auction appears to have been an effective solution to a complex early market design problem