Polygynous marriage is generally more beneficial for men than it is for women, although women may choose to marry an already-married man if he is the best alternative available. We use the theory of biological markets to predict that the likelihood of a man marrying polygynously will be a function of the level of resources that he has, the local sex ratio, and the resources that other men in the local population have. Using records of more than 1 million men in 56 districts from the 2002 Ugandan census, we show that polygynously married men are more likely to own land than monogamously married men, that polygynous marriages become more common as the district sex ratio becomes more female biased, that owning land is particularly important when men are abundant in the district, and that a man's owning land most increases the odds of polygyny in districts where few other men own land. Results are discussed with reference to models of the evolution of polygyny.