%0 Generic
%A Benaim, M.
%A Hofbauer, J.
%A Hopkins, E.
%C London, UK
%D 2006
%F discovery:14516
%I ESRC Centre for Economic Learning and Social Evolution
%K JEL classification: C72, C73, D83. Games, learning, best response dynamics, stochastic fictitious play,  mixed strategy equilibria, TASP
%N 213
%T Learning in games with unstable equilibria
%U https://discovery.ucl.ac.uk/id/eprint/14516/
%X We propose a new concept for the analysis of games, the TASP, which gives  a precise prediction about non-equilibrium play in games whose Nash equilibria  are mixed and are unstable under fictitious play-like learning processes. We  show that, when players learn using weighted stochastic fictitious play and so  place greater weight on more recent experience, the time average of play often  converges in these “unstable” games, even while mixed strategies and beliefs continue  to cycle. This time average, the TASP, is related to the best response  cycle first identified by Shapley (1964). Though conceptually distinct from Nash  equilibrium, for many games the TASP is close enough to Nash to create the appearance  of convergence to equilibrium. We discuss how these theoretical results  may help to explain data from recent experimental studies of price dispersion.