Possible Insight

In our last episode, I sketched out the goals for my new model of the firm. In this post, I’ll present the high level view of my model, which I call “Market Space” (yes, we’ll be using a high-dimensional space again).

High-Level Problem

To begin, let’s put ourselves in the shoes of a CEO at a significantly-sized firm. Assume her incentives are such that her primary goal is for the firm to “succeed”, setting aside the precise definition of “success” for the moment. I think it’s safe to say that any decisions she makes or actions she takes today won’t have an instant effect on “success”. Her immediate options are mostly constrained by decisions the firm has made in the past. Such constraints almost certainly prevent much effect on results for this week and mostly for this month. They probably limit the impact at least somewhat for this quarter and even for this year.

As we move down the organizational chart, people will typically have slightly more immediate effect on their own unit’s success, but their decisions and actions will contribute correspondingly less to the firm’s overall performance. Of course, everyone with decision-making authority undoubtedly realizes that success requires planning so they make decisions and take actions today that give them the best options in the future. Clearly then, our model of the firm must be forward looking and address how the firm allocates resources to achieve future gains.

High-Level Framework

As in my original PFS hypothesis, I’m going to use the concept of a high-dimensional state space. Such spaces are pretty common in analyzing complex systems. In principle, we can define a state space for any dynamic system that encodes its potential behaviors.

I call the new space Market Space. In the abstract, it has an enormous number of dimensions that capture all possible states of the market. These dimensions cover all possible product features, all possible production technologies, all possible consumer preferences, all possible competitor and partner strategies, all possible macroeconomic conditions, all possible environmental factors, etc.

So, a given point in Market Space defines a particular configuration of product features and the values of all the variables that might affect the success of such a product. Then there’s  some metric of how “good” that point is from the perspective of a particular firm, i.e., there’s a function that calculates this “goodness” from all the other variables.

Over time, decision makers try to steer the firm  to regions of Market Space that maximize the chances of “success”. They try to discover product configurations that both fulfill consumer preferences and that the firm can build using efficient product technologies. This process involves such activities as testing primitive versions of products, forecasting changing preferences, and developing new technologies. The goal is to end up in a “good” region of Market Space. [Hat tip to Eliezer Yudkowsky for the idea of “steering the future” to a desired region of a state space. See Section 1.1 of this paper.]

High-Level Visualization

While Market Space is impossible to visualize in all of its dimensions, I thought the admittedly amateurish figure below might help. The three axes represent all the dimensions of Market Space that affect “goodness”. Blue represents how “good” a point is for a firm. As you can see from all the white space, I think most of Market Space consist of points that aren’t any good. No demand for that combination of features, too expensive to manufacture, requires non-existent infrastructure, etc. There are a some “islands” that are pretty good and a few that are very good. So a firm is trying to find these islands among all the “white space”. Once it finds a positive point, it wants to explore that “bubble” and occupy the “best” points.

Initial Complications

Unfortunately, there are two obvious complications. First, competitors. The figure above represents the situation assuming the firm is alone in the market. In reality, competitors will have also staked out positions in Market Space. The next figure shows the current occupation of Market Space for our target firm in green and those of two competitors in yellow and red. From the perspective of the green firm, the occupation of “good” points by the yellow and red firm greatly decrease the potential “goodness” of occupying those points because it will have to split the “goodness”. Moreover, points near the red and yellow firms aren’t as “good” either because they are the obvious places for red and yellow expansion.

The second complication is uncertainty. As anyone who has worked in a firm knows, it’s hard to precisely predict how much profit it will make next quarter from a product it’s been making for years, let alone a new product. So while the blue shows how “good” a point really is, our target firm doesn’t know that value. It only knows its estimated value. But estimation error means that it thinks some white points are blue, some blue points are white, and many blue points are different shades than they really are.

The high-level idea here is that a firm is trying to simultaneously explore and occupy as much blue as possible over time, all the while knowing (a)  that competitors will also try to take over any points that they think are blue and (b) that its internal map of blue regions has limited accuracy. Exploration and occupation both require resources, so it has to allocate those efforts as best as it can given the strategic considerations and uncertain outcomes. Sort of like a big multiplayer real time strategy game. And much like such games, moves one makes in early rounds can dramatically affect opportunities in later rounds.

In the next post, I’ll try to characterize this game in terms of a well-studied problem.