Repeated games with decreasing marginal returns
It seems to me that this will not make a difference if you only consider pure strategies. Consider that player $i$'s winnings is $x$ and from this he gets utility $U_i(x)$. As long as $U_i()$ is increasing in $x$ player $i$ will prefer outcomes with larger winnings to lower ones, which is exactly what he would do if he had constant marginal returns.

Another way of forming this argument is that as long as $U_i()$ is increasing another utility function representing the same preferences over outcomes would be $\hat{U}_i(x) = x$. (You can perform a monotone transformation that transfers $U_i()$ to this.)