Mate selection in monogamous species is typically characterized by female choice, possibly after males compete to establish their fitness. However sometimes the males are also choosy, a case we call mutual choice. In some species either type of mate selection may occur, depending on environmental and population factors. In this paper we seek to determine which form of mating process will arise in terms of two factors: the male/female sex ratio r and the variation v in female fitness.
We consider a game theoretic model of decentralized mating with common preferences, in which unmated males and females are randomly paired in each period and form a couple if there is mutual agreement to do so; otherwise they go into the next period unmated.. In a simplified model with only three fitness types for each sex, we find that a simple line in (v; r) space separates a region with a single female choice equilibrium from one with a single mutual choice equilibrium. When we allow continuous types, the situation complicates to include a region with one female choice equilbrium and two mutual choice equilibria (one more choosy than the other for both sexes). We compare these equilibria with respect to dynamical stability and a new parameter (which we call Gale-Shapley Instability) which measures the probability that in two randomly chosen couples, the male of one and the female of the other will prefer each other to their mates.
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