I am a very Macro guy, but I need to dive a little in the world of Microeconomics. Specifically, I need to study oligopolies. From the general theory to empirics. Since I do not know the literature, I would like to ask if anybody knows a good starting point. Preferably a paper that explains the strategic interactions between firms operating in a oligopoly.
The basics are of course Cournot, Stackelberg and Bertrand competition, which you can find in any textbook.
If you are referring to needing references for research, then the paper you absolutely must know is Dixit and Stiglitz (1977) "Monopolistic Competition and Optimum Product Diversity". American Economic Review. With over 10k citations, the importance of this paper for research cannot be overstated. Especially for macroeconomics, which interests you, knowing this paper in and out is indispensible. It has been extensively used in international trade (e.g. Krugman's models), economic geography and monetary policy (most DSGE models incorporate it) to name a few fields.
While this paper is a specific form of oligopoly, namely monopolistic competition, it is very general and implicitly incorporates much of Cournot and Bertrand competition models. It is simultaneously relatively simple and tractable for use.
Most papers use a "light" version of Dixit and Stiglitz, however. If you search for explanations of this model online, you will find a lot of ressources that explain the different (light) versions step by step. I would actually read those before reading the paper.
A good book on the Dixit & Stiglitz model is also Brakman, S. and Heijdra B.J. (eds.) (2004): "The Monopolistic Competition Revolution in Retrospect." Because this model is so important, many interesting parts of Dixit and Stiglitz are also explained in Baldwin, R., Forslid, R., Martin, P., Ottaviano, G. and Robert-Nicoud, F. (2003). "Economic Geography and Public Policy."
You usually won't need to know any other model for applying oligopolies to research problems. An alternative is, however, the Salop (circle) model (Salop, Steven C. (1979), "Monopolistic competition with outside goods", The Bell Journal of Economics, 10). It may have an advantage depending on your setting, but is a bit outdated compared to Dixit and Stiglitz. In my experience Dixit and Stiglitz is preferred by the research community.
I would recommend taking a look at Jean Tirole's "The Theory of Industrial Organization".
This textbook provides a clean exposition of the models of Bertrand, Cournot, Stackelberg, Hotelling, and Salop (read chapters 5 and 7). This will provide a reasonably complete foundation for modern, game theoretic oligopoly theory.