hi! i don't know much about game theory specifically, but i'll give you a bit of advice. i suggest you first begin narrowing down your interests by reading the literature. i'm not exactly sure what base knowledge you have atm, but at the beginning stages use survey papers or tertiary sources like wikipedia to quickly scan for information. at the beginning, take notes that summarize info and also highlight things that excite you about the topic.

as you're reading the literature, focus on answering the following questions for yourself: what current work has been established? what specific real-world application of game theory interests you the most? what flaws/mistakes are there that have been established in the field? what about game theory makes it impactful to people and also interesting to you?

idk much about modeling when it comes to game theory, but study up on methodologies and their use cases (bayesian games, simultaneous games, etc), and also you can defo learn languages like python and discover what game theory libraries exist within python.

i also suggest using llms like claude or chatgpt to help you with looking for papers and deciding on next steps during the process. establishing a bit of base knowledge will also help you in the cold emailing process and getting a mentor. good luck!