Bertrand, Cournot and Hotelling was on the menu. In addition to covering the mechanics of computing equilibria, spent time trying to motivate each model. Cournot is, I think, the hardest. The short version of the story I gave was this. Firms choose their capacities/quantities, then go to a middleman (should have said platform, so much sexier these days) who auctions of their joint output via a uniform price auction. Wholesale electricity markets come close to this story, which allows one to use Cournot to convey the idea of supply (demand) reduction and the scandal of the California power markets.
Hotelling is easier to motivate, and is a useful vehicle to illustrate why they should always `break’ a model to learn something about it. In the standard Hotelling setup, no reservation price is specified for the buyers. Now, allow the two firms to merge and act like a monopolist. The monopolist’s profit function is unbounded! However, you can still write down a first order condition and solve it. Thus, it is also a useful reminder of the dangers of blindly differentiating and setting to zero.
Contrasted Cournot with Hotelling, for example, the effect on consumer surplus when a merger results in a cost reduction for the merged firm. Also provided an opportunity to remind the class about monopoly and evaluating consumer surplus.
Concluded the module on imperfect competition by applying what had been discussed to Amazon vs. Apple vs the publishers. Another opportunity to walk down memory lane with double marginalization and then add a wrinkle involving competition in the downstream market.