Before revision:  We study the differences in the two equations as they pertain to the one-dimensional rock-paper-scissors game . In particular, we show that a constant amplitude traveling wave solution exists for the infinite population case and show how population collapse prevents its formation in the finite population case. This is closely related to recent work by Postlethwaite and Rucklidge on traveling waves in a similar but distinct rock-paper-scissor setting. Additional solution classes in variations of rock-paper-scissors are also studied .
After revision:  We study the differences in the two equations as they pertain to the one-dimensional rock-paper-scissors game .