Before revision:  Intuitively, when a lossless game (e.g. graphical constant-sum game) is coupled with lossless learning dynamic, their interconnection is also lossless, which results in a pendulum-like energy-preserving recurrent behavior, generalizing the results of Piliouras and Shamma ( SODA, 2014 ) and Mertikopoulos, Papadimitriou and Piliouras ( SODA, 2018 ) .
After revision:  Intuitively, when a lossless game (e.g. graphical constant-sum game) is coupled with lossless learning dynamic, their interconnection is also lossless, which results in a pendulum-like energy-preserving recurrent behavior, generalizing the results of Piliouras and Shamma SODA, 2014 ) and Mertikopoulos, Papadimitriou and Piliouras ( SODA, 2018 ) .