We consider the following L player co-operative signaling game. Nature
plays from the set {0,02˘7}. Nature\u27s play is observed by Player 1
who then plays from the set {1,12˘7}. Player 1\u27s play is observed by
Player 2. Player 2 then plays from the set {2,22˘7}. Player 2\u27s play
is observed by player 3. This continues until Player L observes Player
L-1\u27s play. Player L then guesses Nature\u27s play. If he guesses
correctly, then all players win. We consider an urn scheme for this
where each player has two urns, labeled by the symbols they observe.
Each urn has balls of two types, represented by the two symbols the
player controlling the urn is allowed to play. At each stage each
player plays by drawing from the appropriate urn, with replacement.
After a win each player reinforces by adding a ball of the type they
draw to the urn from which it was drawn. We attempt to show that this type of urn
scheme achieves asymptotically optimal coordination. A lemma remains unproved but we have good numerical evidence for it\u27s truth