## Publicly Accessible Penn Dissertations

2013

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Mathematics

Robin Pemantle

#### Abstract

We consider the following \$L\$ player co-operative signaling game. Nature

plays from the set \$\{0,0'\}\$. Nature's play is observed by Player 1

who then plays from the set \$\{1,1'\}\$. Player 1's play is observed by

Player 2. Player 2 then plays from the set \$\{2,2'\}\$. Player 2's play

is observed by player 3. This continues until Player L observes Player

L-1's play. Player L then guesses Nature's 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's truth.

COinS