## Monday, July 13, 2015

### “Rationality” in the Theory of the Firm... Part 4

Previously: Introduction; Part 1; Part 2; Part 3

Having restated their erroneous description of perfect competition and incorrectly declaring that we agree that a logical fallacy exists within the model, the authors continue
Given that the construction of the Marshall model (minus the perfect competition condition imposed by fiat) is also the same as the classical Cournot analysis, Rosnick turns his attention to the Cournot game.
Again, Keen and Standish make no sense whatsoever. Keen agreed that the Marshall model is textbook perfect competition, so the above quote begins
Given that the construction of the textbook model of perfect competition (minus the perfect competition condition imposed by fiat)
What are we to make of anything which would follow such an introduction? Of course perfect competition is imposed by fiat. It is assumed. The only way I make any sense of their statement is to rephrase as
If we remove the assumption of perfect competition from the model and replace it with an assumption that no matter what firms produce that the price will adjust ex post to clear the market, then we wind up with the Cournot model.
This rephrasing is close to accurate. Perfect competition does not assume a fixed number of firms as does Cournot. Again, this kind of thinking had led me to wonder if Keen had meant Marshall equilibrium rather than perfect competition. But firms in neither Cournot nor Marshall equilibrium are assumed to be price-takers so there is no price-taking assumption to contradict. This just adds to the pile of evidence that Keen and Standish are either confused or misleading.

In any case, their fuller quote reads
Given that the construction of the Marshall model (minus the perfect competition condition imposed by fiat) is also the same as the classical Cournot analysis, Rosnick turns his attention to the Cournot game. However, the Cournot game is defined as a single shot game, where firms must make decisions on their output, accept the profit received and that is the end of the game. Again, the model we are critiquing is not that, as firms iteratively set production values and receive profits, thus allowing agents to gain information about each other inductively. Just as semi-cooperative strategies beat totally defecting strategies in iterated prisoner’s dilemma, the same happens in the Marshall model.
Once again, Keen and Standish make hash of several different models. First of all, they fix the number of firms– violating the assumption of free entrance and exit present in perfect competition and the Marshall equilibrium. Indeed, these models may have very different implications if one happens to change the assumptions!

Putting that aside, there are good reasons why a reader might think Keen and Standish are discussing single-shot Cournot. As I discussed in Section 6.1 of my Comment– as did Paul Anglin previously– Keen and Standish fail to fully describe the objectives of a firm in an iterated game. They merely describe the profits a firm may achieve in a single-period. In an iterated game, however, a firm may be interested in sacrificing a little profit in one period for a lot more profit in the next. Without specifying each firm’s particular objective over the course of the entire, iterated game, there is absolutely no way of knowing if any firm is pursing an optimal strategy.

To take an extreme example, suppose the objective of the firm is to obtain the greatest profits in the first period, and damn any subsequent period. Then the iterated game reduces to the single-shot game, and we are indeed back to Cournot. To take another extreme example, suppose the objective of the firm is to maximize profits obtained in the last period of the game. If the number of iterations is finite, then nothing before the last period matters at all, and iterated game again reduces to single shot. If the number of iterations is infinite, then the final period never arrives and they are forever indifferent to their choice of output.

On the other hand, textbook analysis of infinitely repeated games typically have the firms maximizing something like a present discounted value of profits. That is, if the profits for the firm in time $t$ is given by $\pi_t$, then the firm may seek the greatest possible $$\Pi=\sum_{t=0}^\infty{\delta^t\pi_t}$$ where $0 < \delta < 1$. When applied to the (infinitely-repeated) Cournot-Nash game, profit-seeking firms may fall into an amazing variety of strategic, competitive equilibria. One of these even results in the firms producing at the collusive level without collusion. This result is not unknown to the economics mainstream. If this is all that Keen and Standish mean to say, it is unfortunate that they insist on making such a flawed argument to get there. The failure to describe firm objectives in anything but single-period terms misleads the reader and leaves their position entirely unsupported.

If I misunderstood and Keen and Standish do accept the validity of the textbook analysis of (single-shot) Cournot-Nash, then that is wonderful. It is unfortunate then, that they go on to make such a mess of a defense of infinitely-repeated Cournot-Nash. In Part 5 I will detail the problems with their proposed dynamics as described in their response.

Read my original Comment (including Technical Appendix) at World Economic Review.