Long-run average payoff
= Long-run average payoff
{title2=$\lim_{T\to\infty}T^{-1}\sum_{t=0}^{T-1}u_i^t$}
A <repeated game> criterion evaluating the average stage <payoff> over increasingly long horizons. State how paths without a limit are treated, for example by using a lower limit. Changing a finite prefix does not change a convergent <long-run average payoff>. Thus a one-time gain can be outweighed by permanent future punishment without specifying a discount factor.