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The Stable Marriage Problem (SMP) has been extremely discussed in theliterature and it is useful to a number of real-world applications. We proposea generalized version of the SMP in which numbers of the matching groups aredifferent as in [9]. However, we go further to make a percentage of each groupbehave as active message senders. As such, the special case in which all Malesare active messengers (beta = 1) and all Females are not active (alpha = 0)replicates the results in [9]. Moreover, we use numerical simulation to presentthree cases (and their extremes) in which we vary the percentage of activemessengers in each group. Whereas we are able to replicate previous work, ournumerical simulations also suggest that socially optimal comes only when thegroups are homogeneous. More real-world like results are presented when membersfrom both groups are active message senders.

Heterogeneity and Instability in the Stable Marriage Problem