Repeated games in networks, communication, and Folk theorems
Abstract.
We consider repeated games with imperfect monitoring, in which
each player has a number of neighbors with whom he can communicate:
at each stage, a player can send non costly messages to his
neighbors (communication is unicast: these messages can be different
from a neighbor to another). The payoff the player depends only
on the actions chosen by himself and his neighbors. This structure
is naturally represented by an undirected graph. We make the
assumption that the players can observe their stage payoff but not the
actions chosen by their neighbors. For certain kinds of payoff functions,
we establish a necessary and sufficient condition for the existence of
a protocol able to identify in finite time a player who has deviated,
which leads us to a generalized Folk theorem (characterization of the
set of uniform equilibrium payoffs of the repeated game).