  Oscillatory behaviors are ubiquitous in nature and the human society.
However, most previous works fail to reproduce them in the two-strategy
game-theoretical models. Here we show that oscillatory behaviors naturally
emerge if incomplete information is incorporated into the cooperation evolution
of a non-Markov model. Specifically, we consider a population playing
prisoner's dilemma game, where each individual can only probabilistically get
access to their neighbors' payoff information and store them within their
memory with a given length. They make their decisions based upon these
memories. Interestingly, we find that the level of cooperation generally cannot
stabilize but render quasi-periodic oscillation, and this observation is
strengthened for a longer memory and a smaller information acquisition
probability. The mechanism uncovered shows that there are misperceived payoffs
about the player's neighborhood, facilitating the growth of cooperators and
defectors at different stages that leads to oscillatory behaviors as a result.
Our findings are robust to the underlying structure of the population. Given
the omnipresence of incomplete information, our findings may provide a
plausible explanation for the phenomenon of oscillatory behaviors in the real
world.
