The distribution of age at first marriage shows well-known strong regularities across many countries and recent historical periods. We accounted for these patterns by developing agent-based models that simulate the aggregate behavior of individuals who are searching for marriage partners. Past models assumed fully rational agents with complete knowledge of the marriage market; our simulated agents used psychologically plausible simple heuristic mate search rules that adjust aspiration levels on the basis of a sequence of encounters with potential partners. Substantial individual variation must be included in the models to account for the demographically observed age-at-marriage patterns.