A new framework for equilibrium selection is presented. Playing games recur
rently in space and time may render one of the equilibria "spatially domina
nt". Prevailing initially on a large enough finite part of the space, it wi
ll take over on the whole space in the long run. In particular it will driv
e out the other equilibria along travelling waves. This new dominance conce
pt is compared with the Harsanyi-Selten risk-dominance concept.