In this rather dated video (back from 2011) prof. Rob Axtell (one of the contemporary gurus of agent-based modeling and general interdisciplinary numerical simulation) talks about the possibilities of agent-based models. He also talks about his work in modeling of the economy with huge number of agents.

Controversial debates are often marked by an emergence of polarized state. In this post we will consider yet another variation of the voter model proposed by a group of German researchers [1], which shows that significant repulsion leads to the polarized fifty-fifty state.

It might sound strange, but statistics and geometry are very much related. Result in one is likely to have some meaning in the other. This time Numberphile has teamed up with another my favorite 3Blue1Brown to explore a game using darts.

As it is assumed that a random (unskilled) player plays the game, his plays simply explore a continuous phase space. Each point in the said phase space corresponding to all possible events in the game. To keep playing the game the player has to satisfy a condition, which provides us a boundary in the phase spaces. Conveniently geometric shape enclosed by the boundary is a ball (or a hyper-sphere). So our problem of calculating probability is reduced to a problem of figuring out the ball's volume in respect to the size of phase space. More details in the video below.

Last time we have proposed the agent-based cobweb model. In certain case price time series of this model exhibit different volatility. So this time we will take a look at price change statistics in this model. As is common for our financial markets posts we will consider probability density functions and spectral density.

Most people hate math and (I would like to claim that) they hate statistics even more, because statistics are often harder to understand than everyday geometry, compound interest or any other everyday math problem. Yet understanding statistics is vitally important for many everyday decisions. While we can't fix the larger problem in just one post, we can suggest an interesting talk by Jennifer Rogers given at the Royal Institution about statistical lies and how not to fall for them.