Let us continue exploring Colonel Blotto game! In an earlier post, we became familiar with the basic premise of the model. Then, we have explored what happens when the castles (battlefields) have different importance. This time, let us consider a scenario with two types of troops: one that is slow and inexpensive, and another that is fast but more costly. What happens if we introduce this heterogeneity? Will you be able to beat AI strategy this time?

A short video on the Colonel Blotto game, which visually introduces the game we have been posting about recently. It implements a couple of straightforward strategies, which gradually grow more sophisticated.

It seems that the "smart colonel" strategy from the video above is similar to the strategy I have implemented to be used by computer opponent in the app from an earlier post.

In an earlier post we have seen basic framework behind the Colonel Blotto game. We have assumed that castles are identical and of equal value. In this post let us consider one of the simplest ways to generalize Colonel Blotto game is to assume that castles are heterogeneous. Can you still find a winning strategy?

Happy New Year! It is time for our yearly reflection. Unexpectedly, we just had another good year on Physics of Risk. At least content-wise. We have published 36 posts (+3 in comparison to the previous year). Half of the posts, 18 in total, were supplemented by interactive materials. Overall trend remains more-or-less stable as can be seen from the plot below.

Fig. 1:The number of posts written in English and still available on this iteration of Physics of Risk (as of the end of 2024). The wide bars represent total number of posts for each year since 2010, while the narrower bars represent a number of posts containing an interactive app.

Exploring random telegraph noise has led us to explore some related topics in statistics. Namely, we have shown that power-law distributions can be manufactured by using mixtures of other distributions. Reviewer comments on our recent paper [1] have prompted a quick look at the core concept in statistical physics - Fermi-Dirac statistics.

Summer vacation has served as a reset. I have restarted with a rant about the state of open science, and general tutorial videos, but quickly switch to a few unrelated topics in statistics and opinion dynamics. Finally, we have started talking about Colonel Blotto game, which we will continue this year. I would also like to write a post or two about another recent paper by me and coauthors from Faculty of Mathematics and Informatics [2]. And then... we will see what comes!

References

• A. Kononovicius, B. Kaulakys. 1/f noise in semiconductors arising from the heterogeneous detrapping process of individual charge carriers. Journal of Statistical Mechanics 2024: 113201 (2024). doi: 10.1088/1742-5468/ad890b. arXiv:2306.07009 [math.PR].
• A. Kononovicius, R. Astrauskas, M. Radavičius, F. Ivanauskas. Delayed interactions in the noisy voter model through the periodic polling mechanism. Physica A 652: 130062 (2024). doi: 10.1016/j.physa.2024.130062. arXiv:2403.10277 [physics.soc-ph].

In an earlier post we have seen basic framework behind the Colonel Blotto game. We have assumed both warlords are equal in their strength, and that the castles are identical and of equal value. So, there are at least two obvious ways to generalize the game. In this post let us consider what happens when warlords differ in their troop count. Does the weaker warlord even have a chance? How can the stronger warlord make use of their superior strength?