Strategic mating with common preferences

We present a two-sided search model in which individuals from two groups (males and females, employers and workers) would like to form a long-term relationship with a highly ranked individual of the other group, but are limited to individuals who they randomly encounter and to those who also accept them. This article extends the research program, begun in Alpern and Reyniers [1999. J. Theor. Biol. 198, 71-88], of providing a game theoretic analysis for the Kalick-Hamilton [1986. J. Personality Soc. Psychol. 51, 673-682] mating model in which a cohort of males and females of various 'fitness' or 'attractiveness' levels are randomly paired in successive periods and mate if they accept each other. Their model compared two acceptance rules chosen to represent homotypic (similarity) preferences and common (or 'type') preferences. Our earlier paper modeled the first kind by assuming that if a level x male mates with a level y female, both get utility -|x-y|, whereas this paper models the second kind by giving the male utility y and the female utility x. Our model can also be seen as a continuous generalization of the discrete fitness-level game of Johnstone [1997. Behav. Ecol. Sociobiol. 40, 51-59]. We establish the existence of equilibrium strategy pairs, give examples of multiple equilibria, and conditions guaranteeing uniqueness. In all equilibria individuals become less choosy over time, with high fitness individuals pairing off with each other first, leaving the rest to pair off later. This route to assortative mating was suggested by Parker [1983. Mate Choice, Cambridge University Press, Cambridge, pp. 141-164]. If the initial fitness distributions have atoms, then mixed strategy equilibria may also occur. If these distributions are unknown, there are equilibria in which only individuals in the same fitness band are mated, as in the steady-state model of MacNamara and Collins [1990. J. Appl. Prob. 28, 815-827] for the job search problem.