Value-behavior inconsistency is robust to promote cooperative behavior in structured populations

The evolution of cooperation is a theme commonly studied in biology, psychology, sociology, and economics. Mechanisms that promote cooperative behavior in structured populations have been intensively studied. However, individuals' values, specifically, their opinions have been rarely taken into account so far. Inspired by cognition dissonance theory, we assume that individuals pay the cost of guiltiness if the behavior is defection but the opinion deviates from defection, and pay the cost of regret if the behavior is cooperation but the opinion deviates from cooperation. For all general stochastic evolutionary dynamics on arbitrary static networks with multiple opinions, we prove in the weak selection limit that: (i) value-behavior inconsistency cost promotes cooperative behavior if and only if the average cost of regret is less than that of guiltiness; (ii) individuals with value-behavior consistency are more abundant than that with value-behavior inconsistency. This is in contrast with other mechanisms that are at work for cooperation for one population structure but not others. Furthermore, it is also validated on an empirical network and for non-weak selection intensity. The value-behavior inconsistency is thus a robust mechanism to promote cooperative behavior in structured populations. Our results shed light on the importance of the co-evolutionary dynamics of opinion and behavior, which opens an avenue for cooperation.