From a strategic viewpoint there can be a lot of routes in order to reach a certain positioning for our company. Thinking in mathematical terms, for a set of managing variables the best route to be chosen would be that one minimizing the money spent. It could be seen as a geodesic curve on a hypersurface (the subset of states that we can reach from our managing actions) of the space corresponding to the variables defining the state of the company.

I am going to draw a simple example to illustrate this fact.

Imagine a simple company with the following function of production:

*o = C x*

Where *o* is offer, *x* amount of raw material

And the following contour conditions from the law of offer and demand:

*d = -A p+dt*

Where *d* is demand, *dt* total demand and *p* price of product.

The state of our simple economy is defined by two variables: *x* (amount of raw material for production) and *p* (price of the product) that define sales and surplus supposing the cost of raw material and the slope of the demand curve are constant. Making equal offer and demand to maximize benefit both variables will be linked and the state of the system will have a lower dimension (when there is no surplus).

*B = Bs-S*

Where *B* is benefit, *Bs* is benefit from sales, and *S* cost of surplus.

Understanding the positioning as the market share that we want to reach, our strategy would be defined by the percentage of demand that we want to serve. This value would define directly the price of the product and the quantity of raw material that we need to get. We have only a degree of freedom to define our strategy of prices if we want to maximize benefit.

There is a natural equilibrium point where the curves of the prices of offer and demand match providing an equilibrium value for the quantity of production, following the law of offer and demand. The optimum value would provide a unique state for our production and prices. Then, as there is only one possible state, there is not any need of a price strategy. In markets at perfect competition, the minimum price would be imposed finally in this way and our sales would be linked directly to the sales of other competitors.

A real economy is much more complex than this one. In a real case, the curve of demand would not be linear. There would be other competitors at the market serving the product, and if the market can be fulfilled by other competitors we cannot take the offer and demand curve as a direct reference of our sales. The cost of raw materials would be under its own curve of offer and demand too. Then, there would be many more variables involved and defining the state of system although we could only act on our price of the product and our amount of raw material for production again.

Thinking in this way we can see that the result of any marketing strategy is, in practice, unpredictable.

Strategy is not a matter of solving a set of equations, but a matter of anticipating the movements of competitors. We need a strategy because we are in competition, in other way we would need only to minimize some cost function.

Strategic thinking requires capability of prediction that it can be got only under certain states. For instance, in the previous example, if the offer of competitors can fulfil the total demand we cannot assume that we can sell something if our prices are not below the prices of competition. We can only predict sales at lower prices. This is what happens in a crisis. In this case, the demand is being reduced and only the companies that bet for reducing prices (modifying the offer curve) can control their own company in the physical sense of the word control. As production costs impose a limit on the price of the product, the strategy that fits better that situation following this economic model is a strategy of cost leading.

And what about innovation? Well, in this case, innovation is not necessarily a drawback, but innovation should be driven to improve production reducing the production cost. Process innovation would be the logic innovation related strategy. This would be to swim with the tide, or the low risk innovation strategy.

A more interesting approach is forgetting mathematical models and using model free techniques to analyze our activity. Risk can be seen as something related to perception or subjective. In the case of we are talking about mathematical risk, considering risk as not objective can be considered valid too because although mathematical risk is not observer dependent, is model dependent. Sometimes to swim against the tide can produce better results than with the tide.

If we look back the previous example, the problem with predictability is related to a fulfilled demand, then, a product innovation strategy can be a solution too, because a new product will have a new and not fulfilled demand. What are the pros and cons of this? They are obvious. Although the demand was not be very high, you can select a high price strategy that you cannot use before avoiding the limits imposed by the cost of production, and less competition can imply less complexity (less variables and uncertainty to be considered to define the state of the business), as the initial example showed.

Mature markets can become more complex than novel ones because there is a natural trend to increase entropy in every system as time goes by.

A product innovation strategy, even in a crisis, can provide simpler businesses than a cost leading strategy although many people can think that it should be swimming against the tide. The important thing is to find the proper market or market niche. Probably, they are right with the comparison. As swimming against the tide, you will need the required energy to do it, or in economic terms, the required money to do it. Sometimes, there are not only better or worse strategies but realizable and unrealizable ones too.

Swimming with the tide is comfortable, but comfort usually is not synonym of survival, because not all the competitors can win following the same strategy. The best soldiers are trained to accomplish task under the worst conditions, and there is a good reason for this.