lations 23 is a regular graph of degree k = 2. Games on cycles have been studied by many authors including Ellison (1993), Nalcamaru et al (1997), Ohtsuki et al (2006) and Ohtsuki & Nowak (2006a). The following result can be found in Ohtsuki Sc Nowak (2006a) and holds for weak selection. For DB updating an