"The expected payoff for GRIM versus GRIM is nR. The expected payoff for ALLD versus GRIM is T+(m-1)P. If nR>T+(m-1)P then ALLD cannot spread in a GRIM population when rare."
"…it is more natural to consider a repeated game with a probability w of having another round. In this case, the expected number of rounds is 1/(1-w), and GRIM is stable against invasion by ALLD provided w>(T-R)/(T-P)."
Why is EV 1/(1-w)? Draw the event tree and write out the equation for expected value. The first few terms are