See, the problem with the economic argument is that it's exactly like the argument for N-round prisoner's dilemma resulting in both parties defecting every round starting from the first: it works in theory, but fails utterly in practice because of bounded rationality and foggy information issues. The thing is, real life is not accurately modeled by a scenario where N people are sitting in a room, everyone has perfect information, and things happen slowly enough for exactly the minimum number of contributions to get made and for things to stop there.
A more accurate model of real life is a fog: everyone else will participate or not participate with some probability, out of those individual probabilities you can get a distribution for the collective total (a Gaussian with median V and variance sqrt(N)), and given that distribution you can determine your probability of being pivotal and thus decide the outcome. The mathematical conclusion, that dominant or standard assurance contracts work only for public goods with a return factor greater than sqrt(N), follows as in my above linked forum post.
Now, that's a one-round scenario where everyone either puts their funds in at the start or does not. There are two kinds of multi-round scenarios:
1. You can withdraw your contribution
2. You can't
In the first case, the expected result is that the total donation will end up buzzing around V, as if it is higher it is rational to withdraw and if it is lower it is rational to pledge, but eventually there is going to be a "last round" due to a deadline and network latency bounds, at which point the game is equivalent to a one-round scenario. In the second case, it makes sense to wait until you have more information before doing everything, so everyone will wait until the last second before either participating or not participating. Thus, in both cases my Gaussian model still works.
A more accurate model of real life is a fog: everyone else will participate or not participate with some probability, out of those individual probabilities you can get a distribution for the collective total (a Gaussian with median V and variance sqrt(N)), and given that distribution you can determine your probability of being pivotal and thus decide the outcome. The mathematical conclusion, that dominant or standard assurance contracts work only for public goods with a return factor greater than sqrt(N), follows as in my above linked forum post.
Now, that's a one-round scenario where everyone either puts their funds in at the start or does not. There are two kinds of multi-round scenarios:
1. You can withdraw your contribution
2. You can't
In the first case, the expected result is that the total donation will end up buzzing around V, as if it is higher it is rational to withdraw and if it is lower it is rational to pledge, but eventually there is going to be a "last round" due to a deadline and network latency bounds, at which point the game is equivalent to a one-round scenario. In the second case, it makes sense to wait until you have more information before doing everything, so everyone will wait until the last second before either participating or not participating. Thus, in both cases my Gaussian model still works.