The solution to the Tullock rent-seeking game when R > 2: mixed-strategy equilibria and mean dissipation rates

In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R>2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents. An earlier version of this paper circulated under the title, No, Virginia, There is No Overdissipation of Rents. We are grateful to Dave Furth and Frans van Winden for stimulating conversations, and for comments provided by workshop participants from the CORE-ULB-KUL IUAP project, Purdue University, Pennsylvania State University, Rijksuniversiteit Limburg, and Washington State University. We also thank Max van de Sande Bakhuyzen and Ben Heijdra for useful discussions, and Geert Gielens for computational assistance. An earlier version of the paper was presented at the ESEM 1992 in Brussels and the Mid-West Mathematical Economics Conference in Pittsburgh. All three authors would like to thank CentER for its hospitality during the formative stages of the paper. The second author has also benefited from the financial support of the Katholieke Universitieit Leuven and the Jay N. Ross Young Faculty Scholar Award at Purdue University. The third author benefitted from visiting IGIER where part of the paper was written. The third author also benefitted from grant IUAP 26 of the Belgian Government

Lichenometric dating (lichenometry) and the biology of the lichen genus rhizocarpon:challenges and future directions

Lichenometric dating (lichenometry) involves the use of lichen measurements to estimate the age of exposure of various substrata. Because of low radial growth rates and considerable longevity, species of the crustose lichen genus Rhizocarpon have been the most useful in lichenometry. The primary assumption of lichenometry is that colonization, growth and mortality of Rhizocarpon are similar on surfaces of known and unknown age so that the largest thalli present on the respective faces are of comparable age. This review describes the current state of knowledge regarding the biology of Rhizocarpon and considers two main questions: (1) to what extent does existing knowledge support this assumption; and (2) what further biological observations would be useful both to test its validity and to improve the accuracy of lichenometric dates? A review of the Rhizocarpon literature identified gaps in knowledge regarding early development, the growth rate/size curve, mortality, regeneration, competitive effects, colonization, and succession on rock surfaces. The data suggest that these processes may not be comparable on different rock surfaces, especially in regions where growth rates and thallus turnover are high. In addition, several variables could differ between rock surfaces and influence maximum thallus size, including rate and timing of colonization, radial growth rates, environmental differences, thallus fusion, allelopathy, thallus mortality, colonization and competition. Comparative measurements of these variables on surfaces of known and unknown age may help to determine whether the basic assumptions of lichenometry are valid. Ultimately, it may be possible to take these differences into account when interpreting estimated dates

A Theoretical Model of a Molecular-Motor-Powered Pump

The motion of a cylindrical bead in a fluid contained within a two-dimensional channel is investigated using the boundary element method as a model of a biomolecular-motor-powered microfluidics pump. The novelty of the pump lies in the use of motor proteins (kinesin) to power the bead motion and the few moving parts comprising the pump. The performance and feasibility of this pump design is investigated using two model geometries: a straight channel, and a curved channel with two concentric circular walls. In the straight channel geometry, it is shown that increasing the bead radius relative to the channel width, increases the flow rate at the expense of increasing the force the kinesins must generate in order to move the bead. Pump efficiency is generally higher for larger bead radii, and larger beads can support higher imposed loads. In the circular channel geometry, it is shown that bead rotation modifies the force required to move the bead and that shifting the bead inward slightly reduces the required force. Bead rotation has a minimal effect on flow rate. Recirculation regions, which can develop between the bead and the channel walls, influence the stresses and force on the bead. These results suggest this pump design is feasible, and the kinesin molecules provide sufficient force to deliver pico- to atto- l/s flows.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44478/1/10544_2005_Article_6168.pd

Growth of crustose lichens : a review

Crustose species are the slowest growing of all lichens. Their slow growth and longevity, especially of the yellow-green Rhizocarpon group, has made them important for surface-exposure dating (lichenometry). This review considers various aspects of the growth of crustose lichens revealed by direct measurement including: 1) early growth and development; 2) radial growth rates (RGR, mm yr−1); 3) the growth rate–size curve; and 4) the influence of environmental factors. Many crustose species comprise discrete areolae that contain the algal partner growing on the surface of a non-lichenized fungal hypothallus. Recent data suggest that 'primary' areolae may develop from free-living algal cells on the substratum while 'secondary' areolae develop from zoospores produced within the thallus. In more extreme environments, the RGR of crustose species may be exceptionally slow but considerably faster rates of growth have been recorded under more favourable conditions. The growth curves of crustose lichens with a marginal hypothallus may differ from the 'asymptotic' type of curve recorded in foliose and placodioid species; the latter are characterized by a phase of increasing RGR to a maximum and may be followed by a phase of decreasing growth. The decline in RGR in larger thalli may be attributable to a reduction in the efficiency of translocation of carbohydrate to the thallus margin or to an increased allocation of carbon to support mature 'reproductive' areolae. Crustose species have a low RGR accompanied by a low demand for nutrients and an increased allocation of carbon for stress resistance; therefore enabling colonization of more extreme environments

Wireless, high-bandwidth recordings from non-human primate motor cortex using a scalable 16-Ch implantable microsystem

A multitude of neuroengineering challenges exist today in creating practical, chronic multichannel neural recording systems for primate research and human clinical application. Specifically, a) the persistent wired connections limit patient mobility from the recording system, b) the transfer of high bandwidth signals to external (even distant) electronics normally forces premature data reduction, and c) the chronic susceptibility to infection due to the percutaneous nature of the implants all severely hinder the success of neural prosthetic systems. Here we detail one approach to overcome these limitations: an entirely implantable, wirelessly communicating, integrated neural recording microsystem, dubbed the Brain Implantable Chip (BIC)