  Motivated by the fact that the same social dilemma can be perceived
differently by different players, we here study evolutionary multigames in
structured populations. While the core game is the weak prisoner's dilemma, a
fraction of the population adopts either a positive or a negative value of the
sucker's payoff, thus playing either the traditional prisoner's dilemma or the
snowdrift game. We show that the higher the fraction of the population adopting
a different payoff matrix, the more the evolution of cooperation is promoted.
The microscopic mechanism responsible for this outcome is unique to structured
populations, and it is due to the payoff heterogeneity, which spontaneously
introduces strong cooperative leaders that give rise to an asymmetric strategy
imitation flow in favor of cooperation. We demonstrate that the reported
evolutionary outcomes are robust against variations of the interaction network,
and they also remain valid if players are allowed to vary which game they play
over time. These results corroborate existing evidence in favor of
heterogeneity-enhanced network reciprocity, and they reveal how different
perceptions of social dilemmas may contribute to their resolution.
