Security, Topological Game Theory & Ricci Flow

Hey guys,

Thanks again for around 40,000 views of my last post. It's pretty cool to get these many views for a nerdy blog. And apologies, I have been super-busy at work, writing books, research papers, articles, giving guest lectures etc.

This post is for Perelman, Dr Yau, Melanie Weber, Cao and Zhu, Dr. Fefferman & all nerds who understand my Ricci Flow Video on youtube.. This is my entry into the Field prize Math Video Contest ..win win win.. - https://www.youtube.com/watch?v=z_pjsJisdHQ&t=6s  )...

Here you go... 

1. Amazing Amazing book by Milind Tambe on Security and Game Theory: Algorithms, Deployed Systems - https://www.amazon.com/Security-Game-Theory-Algorithms-Deployed/dp/1107096421 

The book provides detailed overview on

1. Game theoretical framework for security measures,
2. Intelligent Randomization over routes,
3. Bayesian Stackelberg Games,
4. Robust Game Theory,
5. Bayesian Nash Equilibrium,
6. Strategic Security Allocation in Transport networks,
7. Randomization with partial adversary model,
8. Stackelberg vs Nash in security games

2. I want to push this book and concept further in terms of Ricci Flow, Evolutionary Game theory & Security measures - 

Evolutionary game theory is a continuous model with interactions (frequency dependent selection). e.g. the classical Lotka-Volterra predator-prey system fits into this framework. Another example is an infinite population of people playing the game rock-paper-scissors in continuous time. Obviously, if almost everyone is playing rock, the trend will be for more people to play paper. Asymptotic behavior, Nash equilibria and stability of fixed points are studied.

This framework may also be used to analyze the evolution of geometric structures. The Ricci flow is exactly a “replicator equation of quadratic type” for evolutionary game theory. New evolutionary models for various types of geometric flows are put forward.

Hence application of Evolutionary game theory, the classical Lotka-Volterra predator-prey system with The Ricci flow as exactly a “replicator equation of quadratic type” for evolutionary game theory for defense strategy. 

For Example - 

Defense Strategy Selection Model Based on Multistage Evolutionary Game Theory - https://www.hindawi.com/journals/scn/2021/4773894/

The existing network attack and defense analysis methods based on evolutionary games adopt the bounded rationality hypothesis. However, the existing research ignores that both sides of the game get more information about each other with the deepening of the network attack and defense game, which may cause the attacker to crack a certain type of defense strategy, resulting in an invalid defense strategy. The failure of the defense strategy reduces the accuracy and guidance value of existing methods.

3. Ricci Flow and Community Detection for defense and fraud detection. My video is self explanatory -

https://www.youtube.com/watch?v=z_pjsJisdHQ&t=6s 

The community detection application is not only limited to fraud detection but also for applications on biological networks, protein-protein networks, metabolic networks, and gene networks, etc.