Cournot Duopoly - Oligopoly and Foundations of Game Theory

In all my previous undergrad economics courses, we've always discussed oligopolies with OPEC and oil being great examples. However, in our managerial economics class, we've actually started applying some basic math to the model. It's simply expressed as:

P = a - b(Q1 + Q2)
MR1 = a - bQ2 - 2bQ2
MR2 = a - bQ1 - 2bQ2

An interesting point raise by a student was: "Why do we learn these models if we can't necessarily always apply them quantitatively in real life?" and our professor came up with a brilliant answer: "I would hope that especially with your FIT class, you should be able to understand that models are intended simply as a simplification and can help you understand relationships even if you don't always use hard numbers."

Another interesting new way to think we've been introduced to is the Q1 v Q2 graph (explicity not to be confused with a downward sloping demand curve) and is described as a graph of Firm 1's Best-Response Function. Something which I tripped on just now in class was understanding the x intercept (Q1 m - what firm 1 would produce if Q2 produced nothing, a monoploy like scenario) and y intercept (what quantity Q2 would have to produce to kick Q1 out of the market).

I guessed that the y-intercept was the same as the x-intercept which was wrong, because I made some gross assumptions (cost curves of both companies are the same). Whereas, the truth is that firm 2 would have to have a much better MC curve by completely pushing out firm 1 at Q2m. If the cost curves were the same, there would probably be a more balanced production quantitiy for both.

It turns out the y-intercept is the (a-c1)/b. Superimposing the Q2 response function, the reverse appears, the y-intercept is Q2m and the x-intercept is (a-c2)/b, where c1 and c2 is the marginal cost for the respective firms.

The prof then goes to show how, with perfect knowledge ("collusion", or assuming each firm knows both response functions), the two firms will naturally return to equilibrium, even if they try to push (or start) to produce any quantity outside of equilibrium. It is very similar to decreasing osciliations about the mean until the signal stabilizes.

He also discusses collusion, monopolies and "cheating" in collusion and how profit seeking entities will look to predictibly optimize their profits with respect to their competitor's (the market's) production decisions.

How does this relate to game theory? If you can predict what your competitor (in the duopoly model... or any model with N players where N is greater than 1) you can make the appropriate arrangements to maximize your profitability in the market. Suddenly, your mutual decisions are "forecastable" according to game theory.

You can even start to understand the case where the firms would actually prefer to merge and perform as a monoploy. And this is the reason and primary concern for anti-trust with the DOJ or Competition Bureau.