We determine equilibrium acceptance strategies in a class of multi-period mating games where individuals prefer opposite sex partners with a close parameter type (one-dimensional homotypic preferences). In each period unmated individuals are randomly paired. They form a couple (and leave the pool) if each accepts the other; otherwise they continue into future periods. We consider models with a fixed cohort group (without replacement) and also steady-state models (with replacement). Unlike the job-search model of McNamara & Collins involving type preferences (maximizing individuals), we find no segmentation of the populations at equilibrium, rather continuous changes of strategy. We find some similarities and some differences with the Kalick-Hamilton simulation model of attractiveness matching in a dating context. In general, we find that at equilibrium all individuals become less choosy (in accepting potential mates) with time, and that individuals with more central types are choosier than those with more extreme types. Copyright 1999 Academic Press.