A Bit of Game Theory

Game theory so-called is an interesting and useful subject, and it's not just about playing games for entertainment. It can be very useful in a wide range of situations. In fact most students of the field would agree that it is mis-named. It would be better if it were called something like “theory of human interactions.” However game theory is the historical name and we are stuck with it. That means that we call such interactions games, be they games like poker or other interactions such as business decisions.

For our purposes here, a good definition of a game is any interaction between people who do not control the actions of others in the game. The theory deals with finding the best course of action when playing such a game. Obviously that means it can apply to business, government, international relations, family life, and a myriad of other areas. Just as obviously I cannot cover the entire subject in a couple of blogs. However I can point out some interesting results.

One useful idea is the concept of “added value” discussed in the book “Co-opetition” by Brandenburger and Nalefuff. In any game your added value is the difference between the value of the entire game with you in it and the game if you do not play. For example if a tire manufacturer were to invent a tire that reduced fuel consumption by 10%, the added value would be the value of the fuel saved.

In most games you can never hope to get more than the value you add. The major exceptions are shysters, criminals, and governments. All of those can take out of a game more than their added value. They do that by taking the value someone else adds. However in honest games participants get no more than they add and usually a lot less. Here is an example, based on one in the book:

Suppose an eccentric millionaire walks up to you and hands you piece of a jigsaw puzzle, along with a toll-free phone number. He tells you, “If you call this number you will be able to talk to Joe who has the matching puzzle piece. I will pay $100 to whoever gives me the matching pair.”

The total value of this game is $100, the amount the millionaire will pay if you and Joe agree to turn in the matching puzzle pieces. But the real question is what added value you have, and what added value Joe has. If either of you pull out of the game and refuse to play, the whole game is worth nothing. The interesting part is that your added value is $100, but Joe's added value is also $100 even though the entire game is worth only $100. You cannot both get your added value. The best compromise would be to split the difference. Joe pays you $50 and you give him your puzzle piece. He then turns the matching pieces in to the millionaire and walks away with the $100. You are each richer by $50.

In a fair game, your added value is the maximum you can expect, but in many cases you will get less than your added value. That is an important idea when entering into any negotiation. You may think that you are adding a certain value to the game and you may be right. However others also add value and the total added value usually exceeds the total value of the game.

A more practical example would be when an employer and his employees divide up the gains from a business, say manufacture of some widgets which bring in sales of a million dollars per year. The employer provides the equipment, the raw materials, and the building. He may even provide the knowledge of how to make widgets. Without the employer nothing gets made and the value of the game is zero. Therefore the employer's added value is the entire value of the game, one million dollars per year.

But wait. The employees do the actual work of making the widgets. If they don't play the game no widgets get made and the value of the game is again zero. The added value of the employees is also one million dollars per year. Clearly employer and employees will not all get of their added value. Should either side insist on one million dollars per year the other will walk away, remove his added value, and the value of the game will be zero. They must reach some compromise in which each gets only part of the added value they provide.

Similar considerations hold for almost any interaction, be it trade, family relations etc. We can only function as a society if we are willing to compromise and settle for less than our added value.

Now that's enough for one day. Next I'll throw an interesting curve-ball at the eccentric millionaire game and see how that applies to life.

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