Project Management and Game Theory
In a previous article, we looked at the difference between planning and strategy. Basically, a Project Manager planning a new project is organizing a set of collaborating stakeholders to carry out work that will be to everyone’s benefit. However, when it comes to strategy, the course of action taken by one player can have negative consequences on the other players and they will respond to your strategy by changing their own.
Trying to maximize your position in the context of competitors is very difficult, especially when you do not know for sure the relative strengths and weaknesses of those you are competing with. In a sense, it is a bit like playing poker. If you do not know what cards your opponents have, then the outcome of your play is uncertain. However, your opponents do not know what you have either, so you are as free to bluff and misdirect as your opponents are.
The dynamics of poker fascinated two of the last century’s leading academics. Computer scientists will be familiar with John von Neumann, while economists will recognize Oskar Morgenstern. They came up with the concept of Game Theory to analyse the factors involved in games like this.
The only restriction the early Game Theories had was that they were based on zero-sum outcomes. In other words, for me to win, you have to lose. This sort of analysis was helpful in business where me increasing market share by five percent means that my competitors lose five percent of the market.
However, there are many situations in the real world where a wider range of outcomes are possible. For instance, I might have a brand that is very appealing to young buyers. I might launch a product that competes in a sector targeted at older customers. My brand may create interest among a younger clientele, leading to a larger overall market that may benefit all players.
This sort of outcome was very well described in a scenario called the Prisoners’ Dilemma. Two people have been arrested at the scene of a crime. They are held in separate interrogation rooms (or interview rooms as the police like to call them these days) with no way of conferring with each other. They are both offered the same alternatives and are left to think about the options and decide.
If they both confess to the crime, they will both get five years in prison. If neither confesses they will both be charged with a lesser crime and are liable to get one year in prison. However, if one person confesses and the other does not, the confessor gets a three-month sentence, but the other prisoner gets ten years.
This really highlights the differences between planning and strategy. It also shows Project Managers how important it is to communicate regularly with their stakeholders. The difficulty for the two prisoners is that they do not know what the other party is going to do. To analyse their options, we can use the “payoff matrix”:
The figures at the top-right corner of the matrix are the consequences of the actions for Prisoner A and those at the bottom-left are those for Prisoner B. For both prisoners, the consequences are the same. However, the range of prison sentences is radically different. If either prisoner confesses, the best outcome is 0.25 years in prison; the worst is five years. However, if a prisoner chooses not to confess, the range is from one year to ten years. So the sensible option is to confess.
Anyone who is a Project Management Professional (PMP)® or anyone studying for the PMP® exam will notice that this Payoff Matrix is somewhat familiar. If you recall Project Risk Management and the Perform Quantitative Risk Analysis process, you will remember a technique called Expected Monetary Value, where we analysed the consequences of decisions using Decision Trees. The Payoff Matrix could be replaced with a decision tree. In fact, the decision tree is probably a better tool as it is more visual and easier to follow when there are several decisions involved and where there are more than two choices.
Both Velopi’s program and project management professional courses include Decision Trees which, as we have seen above, can assist us in deciding on a course of action or a strategy. These courses are held in Dublin, Cork, Limerick and Galway. For more details on these courses, please visit our training page, or contact us directly.
By Velopi Seamus Collins