 Lewis concludes that a necessary condition for agents to be following a convention is that their preferences to follow the corresponding coordination equilibrium be common knowledge (the issue whether conventions need to be common knowledge has been debated recently, cf. Cubitt and Sugden 2003, Binmore 2008, Sillari 2008, and, for an experimental approach, see Devetag et al. 2013, for a connection to the topic of rule-following, see Sillari 2013). So on Lewis’ account, a convention for a set of agents is a coordination equilibrium which the agents follow on account of their common knowledge of their rationality, the payoff structure of the relevant game and that each agent follows her part of the equilibrium.