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

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

A Model of Migration

A simple game-theoretic model of migration is proposed, in which the players are animals, the strategies are territories in a landscape to which they may migrate, and the payoffs for each animal are determined by its ultimate location and the number of other animals there. If the payoff to an animal is a decreasing function of the number of other animals sharing its territory, we show the resultant game has a pure strategy Nash equilibrium (PSNE). Furthermore, this PSNE is generated via "natural" myopic behavior on the part of the animals. Finally, we compare this type of game with congestion games and potential games.

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

A Consumable Money. An Elementary Discussion of Commodity Money, Fiat Money and Credit: Part I

In this paper we present a series of models, all within the context of a simple two-good economy, which bring out the distinctions among the different types of money and financial institutions. The models emphasize the physical properties of the economic goods, moneys, and trading systems. Part 1 covers models in which the money is a consumable storable; the economies in Part 2 use durable money, fiat money, or credit. Under this framework we are able to successfully contrast the role of private money lenders, banks, bilateral credit systems, and credit clearinghouses. We are also able to model the importance of the bankruptcy or default penalty in supporting the use of fiat.Barley, Gold, Fiat and credit, Evolution of money

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