In this review, we present several variations of the Alpern-Reyniers two-sided matching model, with particular application to its biological interpretation as a mate selection game. In this context, the model describes equilibrium behavior in a dynamic game where unmated males and females of various types in a given cohort group are randomly matched in a succession of periods. If they 'accept' each other, they mate permanently and leave the cohort. The models differ in the utility u(x,y) they assign to individuals of type x who mates with one of type y. The two main models assume that (i) individuals prefer mates of similar type, u(x,y)= -|x-y|; or that (ii) they have a common preference for high types, u(x,y)= y. Other applications of the matching model, for example to job search, are only described briefl
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