I read the book "Theory of Games and Economic Behavior" by John von Neumann and Oskar Morgenstern. I think that stock market may be described by game theory. But here are the problems:
- number of players (traders) varies. In this book that number is constant.
- A player may act (e.g. place a limit order) whenever he wants. In this book, the moves are placed in a specific given order.
- This game has infinite time horizon, that is why we can't describe a payoff functions at the end of the game.
I am interested in such description of stock market, that does not involve any chance moves (i.e. moves that are random, that no player can understand its "nature"). Indeed, each move in stock market is a personal move (i.e. a move made by player's will). I focus mostly on short time horizon.
I would be grateful if someone gave me a general game theoretic description of a stock market that solves these problems (1-3). I would also ask for references in books, articles about this topic. Are there any books about game theoretic view on market microstructure?