These are some no-doubt under-informed thoughts on monopsony and labor markets that I've had preparatory to teaching the principles course. In Peter Diamond's first search article, I believe, he briefly discusses a model of search-friction-induced monopoly that is simple but provocative. The idea is (I am embellishing here, so this is loose) take a large number of sellers and we'll say an equal number of buyers. Give each buyer a downward-sloping demand and let marginal cost be constant and identical for each seller. In a competitive equilibrium, the good sells for marginal cost and each seller serves one buyer. Now add search costs for the buyers--it doesn't matter how big or small. If we start from the competitive price, each seller now faces a demand which is downward-sloping in the neighborhood of the competitive quantity at prices between MC +search cost and MC-search cost. Each will then raise price to MC + search cost. But this is not an equilibrium, since with all charging MC+ search cost, each has an incentive to raise price to MC + 2*(search cost). The only symmetric Nash equilibrium has each charging the monopoly price! And the interesting thing is that this is the unique equilibrium for any value of search cost, however small.
Now when we teach monopsony, we start with a single buyer. The idea that labor markets are monopsonistic in this sense is obviously a non-starter, as your students, some of them anyway, will tell you! There are many buyers. But then you might mention search costs on the seller side, and show how they give each buyer a "little bit" of monopsony power, if they are small, which they probably are.
But we can do the analogue to the Diamond idea on the buyer side as well -- or so it seems to me, and get an equilibrium, with positive search costs, however small, in which each firm pays the (low) monopsony wage. So even a little bit of search friction can conceivably produce, for each of many firms, a lot of monopsony power -- in fact, as much monopsony power as a single buyer would have!!
Does anyone know if something like this idea has been applied to labor market monopsony?