Talking Ourselves to Efficiency : Coordination in an Inter-Generational Minimum Game with Private, Almost Common and Common Knowledge of Advice

In this experiment groups of 8 subjects are recruited into the lab and play Van Huyck et al.'s (1990) Minimum Game for 10 periods. After his participation is over each subject is replaced by another agent, his laboratory descendant, who then plays the game for another 10 periods with a fresh group of new subjects so the generations are non-overlapping. Advice from a member of one generation to his successor can be passed along via free-form messages that generation t players leave for their generation t+1 successors. Finally, payoffs span generations in the sense that the payoff to a generation t player is equal to what he has earned during his lifetime plus what their children earn. It was our conjecture that if we played the Minimum Game using such an inter-generational design then, over time, generations would be able to "talk themselves to efficiency" in the sense that after playing the game, if any generation converged to a Pareto-worst equilibrium, they might advise the next generation to choose higher. We find is that it was much harder for societies to "talk themselves to efficiency" than we expected. More precisely, we find that the Pareto dominant equilibrium emerges only in circumstances where advice is not only public but its publicness is common knowledge. Almost common knowledge is not enough