  The rock-paper-scissors game, commonly played in East Asia, gives a simple
model to understand physical, biological, psychological and other problems. The
interacting rock-paper-scissors particle system is a point of contact between
the kinetic theory of gases by Maxwell and Boltzmann ( collision model) and the
coagulation theory by Smoluchowski ( coalescence model). A $2s+1$ types
extended rock-paper-scissors collision model naturally introduces a nonlinear
integrable system. The time evolution of the $2s+1$ types extended
rock-paper-scissors coalescence model is obtained from the logarithmic time
change of the nonlinear integrable system. We also discuss the behavior of a
discrete rock-paper-scissors coalescence model.
