Multi-Dimensional Game Theory in Corporate Strategy
In this article, McKinsey discusses how they created a game theory based model in order to help managers at the European Rail decide what to do in the face of new entrants when the European Union announced that cross-border passenger service would be open to competition in January of 2010. McKinsey helped incumbents in the industry decide what to do based on a model that seems like a more evolved version of what we had in class.
Perhaps the most interesting part of their application to game theory was that their model had more than just two “dimensions.” We can go back to the prisoner’s dilemma to see what this means. In the prisoner’s dilemma it is essentially two dimensional in that there are two people and two strategies each. In McKinsey’s model, there are the two players and their various strategies, but it also takes into account the various environments that these players could be in, almost like a third dimension. For example, instead of just one two by two matrix, they would have at least one for each variation of each of the following factors:
- Total changes in demand, meaning what will happen to demand with each move by an attacker and each response by an incumbent.
- Cost differences, meaning the weight of economies of scale for incumbents compared to the lower operating costs that new players usually benefit from.
- Network advantages
- Price sensitivity
The first factor is particularly interesting as in this case, their model also takes into account an aspect of time that we don’t have in the prisoner’s dilemma as after each player makes their choice in the dilemma, there is no response other than the consequence of their choice. If for example, after either prisoner made their choice, the warden came back with new terms it might be interesting to see at what point a prisoner changed their strategy. The Nash equilibrium in this “game” also depends on time as it would occur when both the incumbent and the attacker settle on a business strategy and eventually, the attacker company would become an incumbent itself.
It would be interesting to see this model programmed or automated, as even if we were to say there are only two options for each of the environment factors, that would create 24 or 16 different matrices if we were to use ones similar to those in the prisoner’s dilemma. However, as each one of these factors is a spectrum, not just an on/off switch, there would be far more than just 16 possible environments for each outcome. This article provided an interesting perspective, as the problems we see in class are all diluted or simplified to very specific scenarios and payoffs, when in real life, almost none of these things are constant. I really enjoyed seeing something highly theoretical like game theory applied to a real life scenario and would want to read more about how to automate this model or even see it done.