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312 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 50, NO. 3, MARCH 2005 Dynamic Fictitious Play, Dynamic Gradient Play, and
 

Summary: 312 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 50, NO. 3, MARCH 2005
Dynamic Fictitious Play, Dynamic Gradient Play, and
Distributed Convergence to Nash Equilibria
Jeff S. Shamma, Senior Member, IEEE, and Gürdal Arslan, Member, IEEE
Abstract--We consider a continuous-time form of repeated
matrix games in which player strategies evolve in reaction to
opponent actions. Players observe each other's actions, but do
not have access to other player utilities. Strategy evolution may
be of the best response sort, as in fictitious play, or a gradient
update. Such mechanisms are known to not necessarily converge.
We introduce a form of "dynamic" fictitious and gradient play
strategy update mechanisms. These mechanisms use derivative
action in processing opponent actions and, in some cases, can
lead to behavior converging to Nash equilibria in previously
nonconvergent situations. We analyze convergence in the case
of exact and approximate derivative measurements of the dy-
namic update mechanisms. In the ideal case of exact derivative
measurements, we show that convergence to Nash equilibrium
can always be achieved. In the case of approximate derivative
measurements, we derive a characterization of local convergence

  

Source: Arslan, Gürdal - Department of Electrical Engineering, University of Hawai'i at Manoa
Shamma, Jeff S. - School of Electrical and Computer Engineering, Georgia Institute of Technology

 

Collections: Engineering