Game Theory in Projects – The Key to Collaboration

Each project is a game. Different people, with often diverging agendas, play a part. How can a project manager align the stakeholders around a common purpose so that they support and make the project successful? The mathematical method of Game Theory suggests a valuable insight.

A Beautiful Mind is a movie I really enjoy. Russell Crowe plays John Nash, a Nobel Laureate in Economics who developed in 1951 the omnipresent today in Game Theory concept called Nash equilibrium. There is a memorable scene in the movie explaining the concept.

Nash is at a bar with other math students. While the others enjoy their drinks, Nash is seated at a separate table covered with books working on his papers. An attractive blond woman enters the bar accompanied by her less attractive friends. The men start discussing how to approach the blonde. They draw Nash in the dispute.

One of the men advocates “every man for himself” approach. The others agree with him that “the father of modern economics” Adam Smith  put it right: the best results come when everyone in the group does what’s good for him.

This is an inspirational moment for Nash who has been struggling to find a truly original idea. He figures out that if all men go for the blonde, they will be blocking each other and chances are that nobody will get her. Then they will turn to her friends but will be rejected as nobody wants to be a second choice. Nash suggests that best approach would be that the men go not for the blonde but for her friends. “The best results for the group”, says Nash, “come when everyone in the group does what’s good for him and the group.” Adam Smith is wrong.

Such situation in which nobody can get a better result for himself by unilaterally changing his strategy while the strategies of the others remain unchanged is called a Nash equilibrium. It is a stable arrangement which is beneficial for all.

Now let’s think of your project team. How can you as a project manager make sure that everybody will be pulling in the same direction to successfully complete the project? The answer according to Game Theory is that a project manager should always seek to achieve and maintain a Nash equilibrium – or a Win-Win arrangement for each team member and the team. He or she also has to communicate properly why it is beneficial.

This is perhaps a complicated way to say that if throughout a project every team member has the understanding that he or she benefits most when doing what is also best for the team then the work will go smoothly. It is reassuring though to know that abstract math confirms an important principle of human relations. Isn’t it?

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