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We study the evolution of conventions in a well-mixed population engaged in a Stag Hunt game. Results for two pairwise imitative rules of behaviour are contrasted with each other and with those from a third, non-imitative one, namely best response to the current population state. These rules differ both in terms of their cognitive and information requirements and in terms of the extent to which they allow agents to learn from successful cooperators. Depending on payoffs and on how interactions take place, best response updating can make either the rewarding All Stag equilibrium or the inefficient All Hare equilibrium emerge as the long-run convention. Conversely, pairwise imitation favours the Pareto inferior equilibrium. This finding is robust to the introduction of assortment and to allowing for some heterogeneity in the behavioural rules which agents follow.