I'm new to the topic and have begun reading some of the literature out there. I have been trying to find examples of a type of game to see if it already exists but did not have much luck.
Are there examples of two player cooperative games where Player A can communicate with Player B but Player B cannot communicate with Player A and the goal is to maximize their cumulative rewards. Think Player A gets a reward if they communicate helpful information to Player B and Player B gets a reward if they were able to use the information that Player A gave.
This is the general framework of the game and I've tried to keep it as general as possible to hopefully see if there are multiple examples out there that look at this.
Any insights would be appreciated. Cheers!
What you might be looking for is called a signaling game or the related screening game. Signaling games are two-stage games where player 1, has some private information and moves first. The move of Player 1 is observed by Player 2. Player 2 moves second, possibly getting a "signal" from observing the move of player 1. In a screening game it is reversed player 2, the uniformed actor, moves first.