Evolutionary Games and Computer Simulations

The prisoner's dilemma has long been considered the paradigm for studying the emergence of cooperation among selfish individuals. Because of its importance, it has been studied through computer experiments as well as in the laboratory and by analytical means. However, there are important differences between the way a system composed of many interacting elements is simulated by a digital machine and the manner in which it behaves when studied in real experiments. In some instances, these disparities can be marked enough so as to cast doubt on the implications of cellular automata type simulations for the study of cooperation in social systems. In particular, if such a simulation imposes space-time granularity, then its ability to describe the real world may be compromised. Indeed, we show that the results of digital simulations regarding territoriality and cooperation differ greatly when time is discrete as opposed to continuous.Comment: 8 pages. Also available through anonymous ftp from parcftp.xerox.com in the directory /pub/dynamics as pdilemma.p

Compressed Passive Macromodeling

This paper presents an approach for the extraction of passive macromodels of large-scale interconnects from their frequency-domain scattering responses. Here, large scale is intended both in terms of number of electrical ports and required dynamic model order. For such structures, standard approaches based on rational approximation via vector fitting and passivity enforcement via model perturbation may fail because of excessive computational requirements, both in terms of memory size and runtime. Our approach addresses this complexity by first reducing the redundancy in the raw scattering responses through a projection and approximation process based on a truncated singular value decomposition. Then we formulate a compressed rational fitting and passivity enforcement framework which is able to obtain speedup factors up to 2 and 3 orders of magnitude with respect to standard approaches, with full control over the approximation errors. Numerical results on a large set of benchmark cases demonstrate the effectiveness of the proposed techniqu

Transient Analysis of High-Speed Channels via Newton-GMRES Waveform Relaxation

This paper presents a technique for the numerical simulation of coupled high-speed channels terminated by arbitrary nonlinear drivers and receivers. The method builds on a number of existing techniques. A Delayed-Rational Macromodel is used to describe the channel in compact form, and a general Waveform Relaxation framework is used to cast the solution as an iterative process that refines initial estimates of transient scattering waves at the channel ports. Since a plain Waveform Relaxation approach is not able to guarantee convergence, we turn to a more general class of nonlinear algebraic solvers based on a combination of the Newton method with a Generalized Minimal Residual iteration, where the Waveform Relaxation equations act as a preconditioner. The convergence of this scheme can be proved in the general case. Numerical examples show that very few iterations are indeed required even for strongly nonlinear termination

Contraction analysis of switched Filippov systems via regularization

We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that contrary to previous approaches, our conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application.Comment: Preprint submitted to Automatic

Training and Turnover in Organizations

We present a two-level model of organizational training and agent production. Managers decide whether or not to train based on both the costs of training compared to the benefits and on their expectations and observations of the number of other firms that also train. Managers also take into account the sum of their employees' contributions and the average tenure length within their organization. Employees decide whether or not to contribute to production based on their expectations as to how other employees will act. Trained workers learn over time and fold their increased productivity into their decision whether or not to contribute. We find that the dynamical behavior at the two levels is closely coupled: the evolution of the industry over time depends not only on the characteristics of training programs, learning curves, and cost-benefit analyses, but on the vagaries of chance as well. For example, in one case, the double dilemma can be resolved for the industry as a whole and productivity then increases steadily over time. In another, the organizational level dilemma may remain unresolved and workers may contribute at fluctuating levels. In this case the overall productivity stays low. We also find a correlation between high productivity and low turnover and show that a small increase in training rates can lead to explosive growth in productivity.Comment: 9 pages. Also available through anonymous ftp from parcftp.xerox.com in the directory pub/dynamics as training.p