This paper studies the effect of social relations on convergence to the efficient equilibrium in 2 × 2 coordination games from an experimental perspective. We employ a 2 × 2 factorial design in which we explore two different games with asymmetric payoffs and two matching protocols: “friends” versus “strangers”. In the first game, payoffs by the worse-off player are the same in the two equilibria, whereas in the second game, this player will receive lower payoffs in the efficient equilibrium. Surprisingly, the results show that “strangers” coordinate more frequently in the efficient equilibrium than “friends” in both games. Network measures such as in-degree, out-degree and betweenness are all positively correlated with playing the strategy which leads to the efficient outcome but clustering is not. In addition, ‘envy’ explains no convergence to the efficient outcome.