Stochastic Uncoupled Dynamics and Nash Equilibrium
Sergiu Hart and Andreu Mas-Colell
Abstract
In this paper
we consider dynamic processes, in repeated games, that are subject to the
natural informational restriction of
uncoupledness. We study the almost sure
convergence
of play (the period-by-period behavior as well as the long-run frequency)
to Nash equilibria of the one-shot stage game,
and present a number of possibility and impossibility results.
Basically, we show that if in addition to random experimentation
some recall, or memory, is introduced, then successful search procedures that are
uncoupled can be devised. In particular, to get almost sure convergence to
pure Nash equilibria when these exist, it suffices to recall the last two
periods of play.
Journal of Economic Literature Classification Numbers: C7, D83.
-
Theoretical Aspects of Rationality and Knowledge,
Proceedings of the 10th Conference,
Ron van der Meyden (editor), National University of Singapore 2005, pp. 52-61
[extended abstract]
- Games and Economic Behavior 57 (2006), 2, 286-303
- Simple Adaptive Strategies: From
Regret-Matching to Uncoupled Dynamics, Sergiu Hart and
Andreu Mas-Colell, World Scientific (2013),
Chapter 8, 165-189
Related papers: