Field Experiments on the Effects of Reserve Prices in Auctions: More Magic on the Internet

This paper presents experimental evidence on the effects of minimum bids in first-price, sealed-bid auctions. The auction experiments manipulated the minimum bids in a preexisting market on the Internet for collectible trading cards from the game Magic: the Gathering. They yielded data on a number of economic outcomes, including the number of participating bidders, the probability of sale, the levels of individual bids, and the auctioneerç—´ revenues. The benchmark theoretical model tested here is the classic auction model described by Riley and Samuelson (1981), with symmetric, risk-neutral bidders with independent private values. The data verify a number of the predictions of the theory. A particularly interesting result shows that many bidders behave strategically, anticipating the effects of the reserve price on others?bids.

Orbital dynamics of high area-to-mass ratio spacecraft under the influence of J2 and solar radiation pressure

This paper investigates the effect of planetary oblateness and solar radiation pressure on the orbit of high area-to-mass spacecraft. A planar Hamiltonian model shows the existence of equilibrium orbits with the orbit apogee pointing towards or away from the Sun. These solutions are numerically continued to non-zero inclinations and considering the obliquity of the ecliptic plane relative to the equator. Quasi-frozen orbits are identified in eccentricity, inclination and angle between the Sun-line and the orbit perigee. The long-term evolution of these orbits is then verified through numerical integration. A set of ‘heliotropic’ orbits with apogee pointing in direction of the Sun is proposed for enhancing imaging and telecommunication on the day side of the Earth. The effects of J2 and solar radiation pressure are exploited to obtain a passive rotation of the apsides line following the Sun; moreover the effect of solar radiation pressure enables such orbits at higher eccentricities with respect to the J2 only case

A passive high altitude deorbiting strategy

A deorbiting strategy for small satellites, in particular CubeSats, is proposed which exploits the effect of solar radiation pressure to increase the spacecraft orbit eccentricity so that the perigee falls below an altitude where atmospheric drag will cause the spacecraft orbit to naturally decay. This is achieved by fitting the spacecraft with an inflatable reflective balloon. Once this is fully deployed, the overall area-to-mass ratio of the spacecraft is increased; hence solar radiation pressure and aerodynamic drag have a greatly increased effect on the spacecraft orbit. An analytical model of the orbit evolution due to solar radiation pressure and the J2 effect as a Hamiltonian system shows the evolution of an initially circular orbit. The maximum reachable orbit eccentricity as a function of semi-major axis and area-to-mass ratio can be found and used to determine the size of balloon required for deorbiting from circular orbits of different altitudes. A system design of the device is performed and the feasibility of the proposed deorbiting strategy is assessed and compared to the use of conventional thrusters. The use of solar radiation pressure to increase the orbit eccentricity enables passive deorbiting from significantly higher altitudes than conventional drag augmentation devices

A passive satellite deorbiting strategy for MEO using solar radiation pressure and the J2 effect

The growing population of space debris poses a serious risk to the future of space flight. To effectively manage the increase of debris in orbit, end-of life disposal has become a key requirement for future missions. This poses a challenge for Medium Earth Orbit (MEO) spacecraft which require a large Δv to re-enter the atmosphere or reach the geostationary graveyard orbit. This paper further explores a passive strategy based on the joint effects of solar radiation pressure and the Earth’s oblateness acting on a high area-to-mass ratio object. The concept was previously presented as an analytical planar model. This paper uses a full 3D model to validate the analytical results numerically for equatorial circular orbits first, then investigating higher inclinations. It is shown that for higher inclinations the initial position of the Sun and right ascension of the ascending node become increasingly important. A region of very low required area-to-mass ratio is identified in the parameter space of a and inclination which occurs for altitudes below 10,000 km

Solar radiation pressure augmented deorbiting from high altitude sun-synchronous orbits

This paper discusses the use of solar radiation pressure (SRP) augmented deorbiting to passively remove small satellites from high altitude Sun-synchronous orbits. SRP-augmented deorbiting works by deploying a light-weight reflective inflatable device to increase the area-to-mass-ratio of the spacecraft. The interactions of the orbital perturbations due to solar radiation pressure and the Earth’s oblateness cause the eccentricity of the orbit to librate at a quasi-constant semi-major axis. A large enough area-to-mass-ratio will ensure that a maximum eccentricity is reached where the spacecraft will then experience enough aerodynamic drag at the orbit pericentre to deorbit. An analytical model of the orbital evolution based on a Hamiltonian approach is used to obtain a first guess for the required area-to-mass-ratio to deorbit. This first guess is then used in a numerical propagation of the orbital elements using the Gauss’ equations to find the actual requirements as a function of altitude. The results are discussed and altitude regions for Sun-synchronous orbits are identified in which the proposed method is most effective. Finally, the implementation of the device is discussed. It is shown that passive solar radiation pressure deorbiting is a useful alternative to propulsive end-of-life manoeuvres for future high altitude Sun-synchronous missions

Orbit evolution, maintenance and disposal of SpaceChip swarms

The combined effect of solar radiation pressure and atmospheric drag is investigated for future mission conceptsfor swarms of satellites-on-a-chip (SpaceChips). The natural evolution of the swarm is exploited to perform spatially distributed measurements of the upper layers of the atmosphere. The energy gain from asymmetric solar radiation pressure can be used to balance the energy dissipation from atmospheric drag. An algorithm for long-term orbit control is then designed, based on changing the reflectivity coefficient of the SpaceChips. The subsequent modulation of the solar radiation pressure allows stabilisation of the swarm in the orbital element phase space. It is shown that the normally short orbit lifetime for such devices can be extended through the interaction of solar radiation pressure and atmospheric drag and indeed selected and the end-of-life re-entry of the swarm can be ensured, by exploiting atmospheric drag

Orbit control of high area-to-mass ratio spacecraft using electrochromic coating

This paper presents a novel method for the orbit control of high area-to-mass ratio spacecraft, such as spacecraft-on-a-chip, future „smart dust‟ devices and inflatable spacecraft. By changing the reflectivity coefficient of an electrochromic coating of the spacecraft, the perturbing effect of solar radiation pressure (SRP) is exploited to enable long-lived orbits and to control formations, without the need for propellant consumption or active pointing. The spacecraft is coated with a thin film of an electrochromic material that changes its reflectivity coefficient when a small current is applied. The change of reflectance alters the fraction of the radiation pressure force that is transmitted to the satellite, and hence has a direct effect on the spacecraft orbit evolution. The orbital element space is analysed to identify orbits which can be stabilised with electrochromic orbit control. A closed-loop feedback control method using an artificial potential field approach is introduced to stabilise these otherwise unsteady orbits. The stability of this solution is analysed and verified through numerical simulation. Finally, a test case is simulated in which the control method is used to perform orbital manoeuvres for a spacecraft formation

Public Versus Secret Reserve Prices in eBay Auctions: Results from a Pokemon Field Experiment

Sellers in eBay auctions have the opportunity to choose both a public minimum bid amount and a secret reserve price. We ask, empirically, whether the seller is made better or worse off by setting a secret reserve above a low minimum bid, versus the option of making the reserve public by using it as the minimum bid level. In a field experiment, we auction 50 matched pairs of Pok‚mon cards on eBay, half with secret reserves and half with equivalently high public minimum bids. We find that secret reserve prices make us worse off as sellers, by reducing the probability of the auction resulting in a sale, deterring serious bidders from entering the auction, and lowering the expected transaction price of the auction. We also present evidence that some sellers choose to use secret reserve prices for reasons other than increasing their expected auction prices.

Recombinant Estimation for Normal-Form Games, with Applications to Auctions and Bargaining

In empirical analysis of economic games, researchers frequently wish to estimate quantities describing group outcomes, such as the expected revenue in an auction or the mean allocative efficiency in a market experiment. For such applications, we propose an improved statistical estimation technique called "recombinant estimation." The technique takes observations of the complete strategy of each player and recombines them to compute all the possible group outcomes which could have resulted from different matches of players. We calculate the improvement in efficiency of the recombinant estimator relative to the standard estimator, and show how to estimate standard errors for the recombinant estimator for use in hypothesis testing. We present an application to a two-player sealed-bid auction and a two-player ultimatum bargaining game. In these applications, the improved efficiency of our estimator is equivalent to an increase of between 40% and 200% in the sample size. We discuss how to design game experiments in order to be able to take full advantage of recombinant estimation. Finally, we discuss practical computational issues, showing how one can avoid combinatorial explosions of computing time while still yielding significantly improved efficiency of estimation.