Friday, July 17, 2015

“Rationality” in the Theory of the Firm... Part 8

Previously: Introduction; Part 1; Part 2; Part 3; Part 4; Part 5; Part 6; Part 7

Keen and Standish write
This focuses on the simple agent model we use to explore this issue. Rosnick compares the model to agents dancing in a wagon careering downhill. Whilst poetic, it is not a useful metaphor, chiefly because with the wagon, the system’s dynamics are largely determined by the trajectory of the wagon, not the individual agents, whereas with our model, the dynamic behaviour is completely determined by the actions of the agents.
Here, they misunderstand the story. Each firm is– in their simulations– out of control. The rise or fall in its profits is almost entirely determined by the actions of all its competitors and not at all its own actions. Thus, it is not rational for the firm to make decisions based on the assumption that it is in control. Much of the time a firm thinks it made a decision which raised its profits, the firm actually made the wrong choice. Much of the time a firm thinks it made a decision which lowered its profits, the firm actually made the correct choice. It is a funny kind of rationality, that.

They continue,
In §6.3, Rosnick introduces a variant of our agents where the decision is made to reverse the usual decision with small probability that increases the closer to equilibrium the system is. Undoubtedly, this could be done so as to benefit the agent concerned, to the detriment of the other agents in the system, however this action cannot be considered rational. Rational agents always choose the optimum action — the only time rational agents are permitted to act stochastically is when multiple equally valued courses of action are available.
First of all, in the strategy I laid out in this Section 6.3 the decision to reverse is based not on closeness to equilibrium, but the change in profits from the previous period. That aside, this critique cuts against Keen and Standish. Far from always choosing the “optimum action” their firms make inferior choices quite often. By their own argument, then, their agents are irrational. The whole point of a firm reconsidering is to avoid letting the rest of the industry fool it into making inferior choices. There is no reason to rule out stochastic strategies, but even if we disallowed those, chance is not required to accomplish the goal. Keen and Standish simply ignore Section 6.4 of my Comment and the entire Technical Appendix. This only points the way, of course. As discussed in Section 6.1 of my Comment and in Part 4 Keen and Standish still leave undefined the infinite-horizon utility for the firm; without knowing how the firm aggregates profits accumulated over the entire course of the game, there is no way to prove that it has employed an optimal strategy to maximize such profits.

This passage does underline the notion that Keen and Standish do not understand the theory they criticize. Agents may be allowed to choose randomly among choices to which it is indifferent. However, agents may not be indifferent between deterministic and stochastic strategies. It may certainly be that a stochastic strategy pays better than a deterministic one. It may also be that a second deterministic strategy pays even better than the stochastic strategy, but that is actually irrelevant; if any strategy pays better than the one suggested by Keen and Standish, then the equilibrium falls apart.

Most importantly, when Keen and Standish concede “this could be done so as to benefit the agent concerned, to the detriment of the other agents in the system” they concede the whole critique. If– given the strategies employed by the other firms– a superior strategy may be found, then a competitive profit-maximizing firm must use the superior strategy. How can it be rational to leave profits on the table for another firm to collect– except by agreeing with other firms that nobody will ruin their good thing by thinking of their own self-interest?

Contrary to the authors’ claim, their firms do not pursue clearly a strategy that is both rational and non-collusive. As best as may be determined in the absence of a clear objective for the full game, either firms fail to recognize that there is money on the table, or they agree with the others to leave it there.


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

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