Some generalizations of a mutual mate choice problem with age preferences

Abstract

This paper considers some generalizations of the large population game theoretic model of mate choice based on age preferences introduced by Alpern et al. [Alpern et al., Partnership formation with age-dependent preferences. Eur. J. Oper. Res. (2012)]. They presented a symmetric (with respect to sex) model with continuous time in which the only difference between members of the same sex is their age. The rate at which young males enter the adult population (at age 0) is equal to the rate at which young females enter the population. All adults are fertile for one period of time and mate only once. Mutual acceptance is required for mating to occur. On mating or becoming infertile, individuals leave the pool of searchers. It follows that the proportion of fertile adults searching and the distribution of their ages (age profile) depend on the strategies that are used in the population as a whole (called the strategy profile). They look for a symmetric equilibrium strategy profile and corresponding age profile satisfying the following condition: any individual accepts a prospective mate if and only if the reward obtained from such a pairing is greater than the individual’s expected reward from future search. It is assumed that individuals find prospective mates at a fixed rate. The following three generalizations of this model are considered: (1) the introduction of a uniform mortality rate, (2) allowing the rate at which prospective mates are found to depend on the proportion of individuals who are searching, (3) asymmetric models in which the rate at which males and females enter the population and/or the time for which they are fertile differ.