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?

In an earlier post, we invited you to coordinate presidential campaign within a simple web game. We have also mentioned that the framework of the web game relates to game theory and the Colonel Blotto game. Let us turn our attention for the next few posts to this classic game. As we will see it contains rich strategic landscape, and has numerous practical applications in various fields, including political campaigning (as previously discussed), warfare (as suggested by its original context), marketing, and even sports.

Here, in this post, will start by discussing the original formulation of the game.

In a few recent posts we have looked at the DeGroot model and its generalizations. In those posts I have mentioned that while the models are somewhat old and could be considered to be classical, they have resurfaced recently in the opinion dynamics literature.

This recent Master thesis is an example of a study conducted using the DeGroot model. Its novelty lies in an exploration of in-group and out-group biases within the framework of the DeGroot model. We invite you to watch the recording of the defense presentation shared by IFISC.