Game Theory and Project Management

Game theory is a branch of applied mathematics. Game theory looks at decision-making amongst groups of people where the outcome for each person or “player” in a given situation or “game” depends on the actions of all.

Game theory attempts to predict an individual's success in decision-making, depending on the choices of others.

If you are a player in a game, when choosing your course of action, you must take into account the choices of others. However, when thinking about their choices, you must recognize that they are thinking about yours, too. As such, when you are coming up with a strategy for decision-making you must take into account your thinking, the thinking of others and, in turn, try to take into account your thinking about the other players' thinking, and so on.

The Prisoners' Dilemma game is a classic example in game theory. Two prisoners are held as suspects in a burglary. Each is offered the following deals:

• If both prisoners confess, then both will serve a prison sentence of three years.

• If one prisoner confesses and agrees to testify against the other, but the other does not confess, then the confessing prisoner will go free, while the silent prisoner will go to jail for five years.

• If neither prisoner confesses, both will go to jail for one year.

The prisoners' best interest is to both say nothing and accept one year each in jail.

The problem is that neither prisoner is sure if the other will confess to avoid jail completely. Game theory tells us that the most likely scenario is both prisoners will confess and serve three years, instead of just one.

Game theory was first developed to predict situations where one player does better at another's expense, the name for this is zero sum games. Today, game theory has expanded to treat a wide range of situations and interactions, including human as well as non-human players (computers, for example). As such, game theory is an excellent tool for project management.

Project managers manage the links between related projects, decide on resource priorities and report progress of the project to the appropriate people. This authority, responsibility and accountability is an important and demanding role. This mostly involves dealing with people; negotiating with them and arriving at a solution that keeps the project moving forward. It is in these negotiations that game theory can be an essential tool for project management.

On a day-to-day basis, project managers need to solve problems to keep projects on track and ensure that all those involved are motivated. As mentioned, this often involves negotiation.

Here are some things that project managers need to think about in any negotiation process:

• What is the issue you are trying to solve?
• Who are the players?
• Which players will have an impact on the success of your decision?

To use game theory for project management, draw a list of players keeping the above questions in mind. For each player then answer the following questions:

• Are there any time issues? Who is in a hurry and and who can afford to delay? Will players make decisions independently or wait for other players make decisions?

• What players can make a commitment to help you and the project? Prioritize these players.

• Have you got angle to negotiate? Mutual gain is possible if players have different preferences, priorities or capacities. Where mutual gain is likely, a negotiated outcome is possible.

• What are the players’ goals? Put yourself in each player’s shoes and assume their goals and actions will be rational from their point of view, even though you may not agree.

It is helpful to put these questions and players in a simple table to clearly show different choices, or tree diagrams that follow steps of an interaction. By looking at the possible outcomes and working backwards, project managers can choose the strategy most likely to give the best results.

Using game theory in the above manner helps you understand how people act and interact – an essential skill needed to successfully manage projects.