  The Stag-hunt game is a prototype for social contracts. Adopting a new and
better social contract is usually challenging because the current one is
already widely adopted and stable due to deviants' sanctions. Thus, how does a
population shift from the current social contract to a better one? In other
words, how can a social system leave a local social optimum configuration to
achieve an optimum global state? Here, we investigate the effect of promoting
diversity on the evolution of social contracts. We considered group-structured
populations where individuals play the Stag-hunt game in all groups. We model
the diversity incentive as a Snow-drift game played in a single focus group
where the individual is more prone to adopt a deviant norm. We show that
moderate diversity incentives can change the system dynamics, leading the whole
population to move from the locally optimal social normal to the globally
optimal one. Thus, an initial fraction of adopters of the new norm can drive
the system toward the new social optimum norm. After the new social contract
becomes the new equilibrium, it remains stable even without the incentive. The
results are obtained using Monte Carlo simulations and analytical approximation
methods.
