 Suppose next that both agents are Bayesian rational, and that part of what each agent knows is the payoff structure of the Intersection game. If the agents expect each other to follow \((s_2, s_2)\) and they consequently coordinate successfully, are they then following a convention? Not necessarily, contends Lewis in a subtle argument on p. 59 of Convention. For while each agent knows the game and that she is rational, still she might not attribute the same knowledge to the other agent. If each agent believes that the other agent will follow her end of the \((s_2, s_2)\) equilibrium mindlessly, then her best response is to follow her end of \((s_2, s_2)\). But in this case the agents coordinated as the result of their each falsely believing that the other acts like an automaton, and Lewis thinks that any proper account of convention must require that agents have correct beliefs about one another. In particular, Lewis requires that each agent involved in a convention must have mutual expectations that each is acting with the aim of coordinating with the other. The argument can be carried further on. What if both agents believe that they will follow \((s_2, s_2)\), and believe that each other will do so thinking that the other will choose \(s_2\) rationally and not mindlessly? Then, say, Liz would coordinate as the result of her false second-order belief that Robert believes that Liz acts mindlessly. Similarly for third-order beliefs and so on for any higher order of knowledge.