We explore the effects of interaction-induced starbursts and of the progressive formation of galaxies on the faint galaxy properties in an OMEGA = 1 cosmology. Interactions and mergers, that brighten and blue of order 1% of galaxies at the present epoch, are expected to increase rapidly with redshift. We show that the resulting brightening of the numerous gas-rich dwarf galaxies at moderately high redshifts could make the galaxy luminosity function depart significantly from the predictions of models which assume standard evolution. Interaction-induced starbursts can in turn explain the observed number-magnitude and number-redshift counts of galaxies in the magnitude range 18 less-than-or-similar-to m(B) less-than-or-similar-to 21. At fainter levels, the model predicts too many observable galaxies at z > 1 if the comoving number density of galaxies is assumed to be constant and equal to that observed today. Allowing for the progressive appearance of galaxies as prescribed by the peak counting formalism, however, helps to reconcile the model with the available data. We conclude that a marginally acceptable model describing the faint galaxy population is that present-day galaxies began to appear in large numbers at z approximately 3 and were thereafter subjected to interactions and minor mergers inducing starbursts, mostly in gas-rich, low-luminosity galaxies, at a rate that declined by about an order of magnitude from z approximately 1 to the present. This scenario can be tested using moderately resolved images of faint galaxies.