Games with Private Information
Every game so far has been played with the matrix face up. Real trading is not like that: you do not know who is on the other side of your quote, and the whole difficulty of market making follows from it.
Types
The standard way to model this is to say each player has a type that only they observe. In a trading context the type is what the counterparty knows: whether they have information about where the price is going, or are simply rebalancing a portfolio.
You cannot see the type. What you can see is the action, and different types act differently, which makes the action informative.
Once information is private, an action is never just an action. It is also evidence about the type of the player who took it, and reasoning that ignores the second half will misprice everything.
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