Cyclic motions in Dekel-Scotchmer Game Experiments

TASP (Time Average Shapley Polygon, Bena{\=\i}m, Hofbauer and Hopkins, \emph{Journal of Economic Theory}, 2009), as a novel evolutionary dynamics model, predicts that a game could converge to cycles instead of fix points (Nash equilibria). To verify TASP theory, using the four strategy Dekel-Scotchmer games (Dekel and Scotchmer, \emph{Journal of Economic Theory}, 1992), four experiments were conducted (Cason, Friedman and Hopkins, \emph{Journal of Economic Theory}, 2010), in which, however, reported no evidence of cycles (Cason, Friedman and Hopkins, \emph{The Review of Economic Studies}, 2013). We reanalysis the four experiment data by testing the stochastic averaging of angular momentum in period-by-period transitions of the social state. We find, the existence of persistent cycles in Dekel-Scotchmer game can be confirmed. On the cycles, the predictions from evolutionary models had been supported by the four experiments.