1. Each player has a set of tiles that each have a particular color and a particular number.
2. The tiles a player has are known only to other players (they are placed to face away from the player)
3. On your turn, you may either place one of your tiles, or give a hint to another player about their tiles.
4. Hints can only take the form of "you have exactly K tiles of C color <indicate the K tiles>" or "you have exactly K tiles of N number <indicate the K tiles>". There are some rules for how many hints can be given and ways to "earn back" more hints to give.
4b. You can make more deductions than what the hints provide. There are a fixed number of each tile. e.g. There are 2 RED-4 tiles. So if you can see that two other players both have a RED-4 tile, this means that you cannot have a RED-4 tile. So if someone gives you the hint that you have a *-4 tile, you know it is not RED. But the two players with the RED-4 tiles cannot see their own, so they cannot make this deduction. But if you act in a way that shows that you have made the deduction, and they are really smart, they can observe your act and deduce that you would have only made that act if you knew that you didn't have a RED-4 tile. And since they can only see 1 other RED-4 tile, they can deduce that they must hold the other.
5. No other communication is allowed.
6. In the center of the table there are stacks for each color that start empty. The goal of the game is to populate the stacks by playing the color tiles of that stack in increasing number. (e.g. RED-1, RED-2, RED-3 ...). If a player tries to play a tile that is invalid (e.g. the RED stack is only up to RED-2 and the player selects their RED-4 tile), a counter is incremented.
7. The game ends when the counter reaches a threshold or all tiles are played. The score is equal to the number of tiles played. Higher is better.
I have long thought that it should be possible to write an AI that does superhuman hint-giving and deduction, provided that all of the AIs can collude beforehand. That is, if all of the AIs have a giant lookup table that essentially says "If the board is in this particular state, and I give hint H, that actually means FOO" where FOO contains more bits of information than hint H would by itself.