Coordinating over time. As well as giving the actual success rates in the full agreement and vector treatments, Figure 1 shows the success rate that would have been achieved in the full agreement treatments if the rules for the provision of the public good had been the same as in the vector treatment (the FULL ALL HP line). Observe that success rates would have been very high. This tells us that very different things are causing inefficiency in the full agreement treatments compared to the vector treatments. In the vector treatments we know that any failure to provide the public good must be caused by the total contribution being insufficient. In the full agreement treatments it is clear that failure to provide the public good was primarily caused by a lack of agreement, and not the total contribution being insufficient. This allows us to reconcile the high contributions we observe in the full agreement treatment (see Table 6) with the not so high success rate (see Table 5). Figure 1 suggests that increasing success in the full agreement treatments reflects groups learning how to coordinate. One way to capture this learning effect is to look at whether group success is permanent or temporary. We know from the previous literature that success in the standard treatment tends to be temporary, i.e. success in one period is no guarantee of success in subsequent periods (Xxxxxxx, Xxxxxxxxxx and Xxxxxxxxx 2013). If groups in the full agreement treatments are learning how to coordinate then we would expect success to be more permanent, i.e. once the group finds how to coordinate they will stick with it. Such a difference between the full agreement and vector treatments would be consistent with Theorem 1 and the notion of collective rationality, provided that groups learn to coordinate on split the cost equally. We find strong evidence that group success is more permanent in the full agreement treatments. For instance, in the full agreement treatments, 27 out of the 52 groups successfully provide the public good in every round after their first success; this meant sustaining success for an average of 6.0 out of ten rounds.27 In the vector treatments, only 6 out of the 51 groups sustained successful provision; they did so for an average 5.3 rounds. This difference is significant for both the unscrambled (LR, p < 0.001) and scrambled treatments (p = 0.06). Also, in the full agreement treatments, initial success was maintained for an average of 4.7 rounds compared to only 3.2 rounds in the v...
