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Summary: Distributed Convergence to Nash Equilibria with Local Utility Measurements
Gurdal Arslan and Jeff S. Shamma
Abstract-- We consider multiplayer repeated matrix games
in which several players seek to increase their individual
rewards by updating their strategies based on limited infor-
mation. One body of work assumes that players can measure
the actions of other players, but do not have access to the
utility functions of other players. In this case, well known
strategy update mechanisms such as Fictitious Play (FP) and
Gradient Play (GP) provide convergence to Nash equilibria in
certain special classes of games. Recent work by the authors
introduced "dynamic" versions of FP and GP, where players
use derivative action to process and respond to the information
available to them. These mechanisms, called derivative action
FP and derivative Action GP, lead to behavior converging to
Nash equilibria in a significantly larger set of games than
standard FP and GP provide. In this paper, we consider the
case where players do not have access to opposing actions. As
before, players do not have access to opposing player utility
functions. Furthermore, a player's access to its own utility
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