Pirate game

Let us imagine five self-interested, rational and bloodthirsty pirates. They have recently found a treasure of 100 gold coins. Now the captain, being the most well-respected, has to propose how to split the treasure among themselves. After he makes his proposal all pirates vote to accept it. If majority of pirates vote yes, then the treasure is split as proposed. But if not, then the captain is executed and new captain is appointed. This new captain will make a new proposal. Having in mind that succession order is known to all pirates devise a strategy for the initial captain. He should retain as much treasure as possible, but stay alive.

Note that if votes are tied, the tie is broken according to captains vote. So we can hint you to start solving the problem backwards. Let us assume that only two pirates are left. In such case captain (P4) could keep all the treasure to himself as votes would equally split (1 on 1). So try to imagine how the previous captain (P3) could have used this information in order to retain his life? What about P2? Original captain? You can try your solution using applet below.

V. Gontis: Going to the roots of econophysics

On 9th of November I have finally left for Boston University. There, at the Center of Polymer Studies, I will spend almost a year working with the most prominent econophysicists (such as H. E. Stanley, who is one of most well cited contemporary physicists). This opportunity to visit Boston University was provided by the Baltic-American Freedom Foundation. H. E. Stanley is one of the founding fathers of "econophysics". 20 years ago he coined this term to describe a new branch of statistical physics, which was primarily interested in financial markets. Contemporary econophysics is rapidly developing field, which now takes up a lot of interest in other socio-economic systems as well as in social behavior observed in biological systems.

Read more on gontis.eu (this article is written in Lithuanian) »

Chaotic dynamics in the kicked rotator problem

Kicker rotator (or rotor) problem is one of the classical examples of dynamical chaos in physics. The focus of this problem is a particle which moves in circular motion (e.g., pendulum on a stick). This particle is being acted upon periodically, lets assume that \( T=1 \), by homogeneous field (e.g., gravitational field, which is being turned on periodically for a brief periods of time). When the field is on, it creates a force, acting on the particle, of strength \( K \). As field is on only for a very brief periods of time, the force may be approximated by the Dirac delta function.