Here's another way to look at it:

Imagine that everyone starts at time t1 with some level of utility, U[n]. Now, they generate a utility based on their beliefs about the sum of everyone else's utility (at time t1). Then they update by adding some function of that summed (averaged, whatever) utility to their own happiness. Let's assume that function is some variant of the sigmoid function. This is actually probably not too far off from reality. Now we know that the maximum happiness (from the utility of others) that a person can have is one (and the minimum is negative one). And assuming that most people's base level of happiness is somewhat larger than the effect of utility, this is going to be a reasonably stable system.

This is a much more reasonable model, since we live in a time-varying world, and our beliefs about that world change over time as we gain more information.