Modeling Epidemic Spread in Synthetic Populations - Virtual Plagues in Massively Multiplayer Online Games

A virtual plague is a process in which a behavior-affecting property spreads among characters in a Massively Multiplayer Online Game (MMOG). The MMOG individuals constitute a synthetic population, and the game can be seen as a form of interactive executable model for studying disease spread, albeit of a very special kind. To a game developer maintaining an MMOG, recognizing, monitoring, and ultimately controlling a virtual plague is important, regardless of how it was initiated. The prospect of using tools, methods and theory from the field of epidemiology to do this seems natural and appealing. We will address the feasibility of such a prospect, first by considering some basic measures used in epidemiology, then by pointing out the differences between real world epidemics and virtual plagues. We also suggest directions for MMOG developer control through epidemiological modeling. Our aim is understanding the properties of virtual plagues, rather than trying to eliminate them or mitigate their effects, as would be in the case of real infectious disease.Comment: Accepted for presentation at Digital Games Research Association (DiGRA) conference in Tokyo in September 2007. All comments to the authors (mail addresses are in the paper) are welcom

Quantum-Monte-Carlo Calculations for Bosons in a Two-Dimensional Harmonic Trap

Path-Integral-Monte-Carlo simulation has been used to calculate the properties of a two-dimensional (2D) interacting Bose system. The bosons interact with hard-core potentials and are confined to a harmonic trap. Results for the density profiles, the condensate fraction, and the superfluid density are presented. By comparing with the ideal gas we easily observe the effects of finite size and the depletion of the condensate because of interactions. The system is known to have no phase transition to a Bose-Einstein condensation in 2D, but the finite system shows that a significant fraction of the particles are in the lowest state at low temperatures.Comment: six pages, two figures; Contribution to QFS98; To be published in Journ. Low. Temp. Phy

Leverage Causes Fat Tails and Clustered Volatility

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing", i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior", such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse.Comment: 19 pages, 8 figure