This book sounds like exactly what you want: Gaming the Market: Applying Game Theory to Create Winning Trading Strategies by Ronald Shelton. It is written from a traders' point of view rather than a quant's.
I also found this old paper very helpful: A Game Theory Analysis of Options: Contributions to the Theory of Financial Intermediation in Continuous ...
They are different trends of research
agent based models, and you are right: Michael is a pioneer
point process based models, and I would say that Frederic's book is a reference: Limit Order Books.
propagator initiated models, here Jean-Philippe's work, and his recent book, is what has to be read: Trades, Quotes and Prices.
Markov-chain based models, ...
Here is a list of books I have and like:
Pretty much every puzzle style question I got in any interviews I'd seen before, essentially from reading books like these.
Simpler puzzles, nicely illustrated.
My Best Mathematical and Logic Puzzles (Dover Recreational Math), Marten Gardner
A nice book of shortish puzzles, harder than ...
These games are usually won by luck.
If there is no fee for buying stocks I'd diversify, i.e. buy many different stocks, to get stable returns. After some weeks you'll see which profit you'll need to beat. Depending on the rules if options are allowed you could invest in highly leveraged derivatives and hope you win. As there is no point not to try to win I ...
There are severa ways you could formulate this problem in game theoretic terms. Hoping this is not too basic an answer for you : from what you write, the two canonical approaches would be to frame things in terms of Cournot oligopolies (firms simultaneously set quantities and prices result from the market clearing condition supply=demand) or Bertrand ...
The field you have in mind is covered with differential game theory, and it game birth to Mean Field Games (MFG), the book posted in a comment is certainly the reference: Probabilistic Theory of Mean Field Games with Applications volume 1 and 2 by Carmona and Delarue.
MFG started with two independent trends of research:
Mean field games by Lasry and Lions
I guess I could give you a far from complete, but good start of researchers who've tried using ML/CS in LOB modeling: Alvaro Cartea, Marcos Lopez de Prado, Sebastian Jaimungal, Dieter Hendricks, Brian Ning, Jean-Philippe Bouchaud (mean-field games, not ML), Rama Cont (used to only do math modeling, but recently tried deep learning for price formation), etc.