In freshman-level economics, we tend to talk about "markets" as though all buyers and sellers costlessly come together and become aware of the price at which they can buy and sell, often with that price simply magically obeying the rule that the amount buyers wish to buy at that price will coincide with the amount that sellers wish to sell. Even when we start talking about models of oligopoly, even at the upper-level undergraduate level, we tend to think about markets where there is a large set of buyers who observe the same prices and more or less simply choose the cheapest product available. The two dominant models in much of economics seem to be something like a Walrasian auction or a continuous-double-auction with competition on both sides, and something in which sellers post prices publicly and buyers take them as given and respond.
In some countries there are large "bazaar" economies with a lot of individual haggling over prices, but they often seem foreign to Americans; there isn't a lot of "bilateral monopoly" haggling in the US aside from the market for houses and cars. These are large purchases of goods in which there is a certain amount of differentiation. Also, that is really only applicable to consumer purchase of goods. A lot of the market for intermediate goods involves procurement divisions of large companies putting out solicitations for bids, or at least trying to negotiate down the per-unit cost of large purchases from vendors.
I think perhaps this hasn't received as much attention from economists; at least not from the ones I've read. My simple go-to mental model of firms involves their trying to generate enough gross profit (i.e. revenues minus the direct cost of selling an item) to cover their fixed costs (basically any cost that isn't "direct"). In a context of two firms negotiating over what amounts to gains-from-trade, the firms are ultimately bargaining over which of them gets to apply what portion of the gains to its own overhead costs and/or final profit.
This post, more even than most of the things I post here, is mostly as a reminder for me to come back to if I find myself casting about for a research idea someday. I think there's something in here, but I'm not sure what.
 There is some discussion of "price discrimination", but even that is generally done on a large, statistical basis, with buyers still acting as "price-takers".