  We study the effects of individual perceptions of payoffs in two-player
games. In particular we consider the setting in which individuals' perceptions
of the game are influenced by their previous experiences and outcomes.
Accordingly, we introduce a framework based on evolutionary games where
individuals have the capacity to perceive their interactions in different ways.
Starting from the narrative of social behaviors in a pub as an illustration, we
first study the combination of the prisoner's dilemma and harmony game as two
alternative perceptions of the same situation. Considering a selection of game
pairs, our results show that the interplay between perception dynamics and game
payoffs gives rise to non-linear phenomena unexpected in each of the games
separately, such as catastrophic phase transitions in the cooperation basin of
attraction, Hopf bifurcations and cycles of cooperation and defection.
Combining analytical techniques with multi-agent simulations we also show how
introducing individual perceptions can cause non-trivial dynamical behaviors to
emerge, which cannot be obtained by analyzing the system as a whole.
Specifically, initial heterogeneities at the microscopic level can yield a
polarization effect that is unpredictable at the macroscopic level. This
framework opens the door to the exploration of new ways of understanding the
link between the emergence of cooperation and individual preferences and
perceptions, with potential applications beyond social interactions.
