 Schelling’s Department Store problem of Example 1.5 is a very simple example in which the agents “solve” their coordination problem appropriately by establishing a convention. (see also the entry on  convention  in this encyclopedia.) Using the vocabulary of game theory, Lewis (1969) defines a convention as a strict coordination equilibrium of a game which agents follow on account of their common knowledge that they all prefer to follow this coordination equilibrium in a recurrent coordination problem. A coordination equilibrium of a game is a strategy combination such that no agent is better off if any agent unilaterally deviates from this combination. As with equilibria in general, a coordination equilibrium is strict if any agent who deviates unilaterally from the equilibrium is strictly worse off. The strategic form game of Figure 1.3 summarizes Liz’s and Robert’s situation. The Department Store game has four Nash equilibrium outcomes in pure strategies: \((s_1, s_1),\) \((s_2, s_2),\) \((s_3, s_3)\), and \((s_4,  s_4)\).[21]  These four equilibria are all strict coordination equilibria. If the agents follow either of these equilibria, then they coordinate successfully. For agents to be following a Lewis-convention in this situation, they must follow one of the game’s coordination equilibria. However, for Lewis to follow a coordination equilibrium is not a sufficient condition for agents to be following a convention. For suppose that Liz and Robert fail to analyze their predicament properly at all, but Liz chooses \(s_2\) and Robert chooses \(s_2\), so that they coordinate at \((s_2, s_2)\) by sheer luck. Lewis does not count accidental coordination of this sort as a convention.