## Tuesday, November 16, 2010

### A Bit More Game Theory

Remember the eccentric millionaire who handed you a puzzle piece and offered \$100 for that plus its matching piece? He's back, this time with a twist. First he informs you that you were not the only player in the last game. He actually handed out 100 identical pieces, scattered around the country so players could not know the others who were playing. Joe had 100 identical matching pieces. All 100 pairs were turned in so the millionaire paid out a total of \$10,000. The players were sensible so Joe walked away with half of that, \$5,000. The other players got the other half, \$50 each. Everybody got half of his added value.

Our rich if slightly crazy friend now wants to play the game again, but with a difference. Again you have one of the 100 puzzle pieces scattered around the country. However this time Joe only has 95 pieces but he knows there are 100 pieces out there to match his. Five players are going to get left out. The total value of the game is now only \$9500. Joe's added value is again the entire value of the game, this time \$9500, but what is your added value now? If you pull out of the game how is does that change the total value?

Well, if you pull out that leaves Joe with his 95 pieces but there are 99 others with whom he can negotiate. You cannot change the value of the entire game so your added value is zero. You have no negotiating power at all unless you can contact the other players and negotiate as a group. Joe has all the power and if he offers you a dollar for your puzzle piece you might as well take it. In fact if he offers you a dime you might as well take that. If you don't, somebody else probably will and you will be one of the five players who get nothing. Joe is negotiating with people who have no added value.

Does this happen in real life? You better believe it. Some businesses make sure that they never quite fill demand. That leaves them with the power to set the price, subject only to the maximum people are willing to pay. Of course that works only when those businesses have an effective monopoly. They may have patent protection or their product may be the “in” thing, people believe that they must have not only the product but a particular brand name. It also happens in franchise businesses which limit franchisees so they don't compete with each other. And it happens in entertainment.

Movie stars provide a good example. When a director looks to hire actors he must look at how many people will pay to see the movie. He may find a wonderful unknown actor willing to work for a pittance to get the exposure. However he will prefer the star, the well-known veteran who is popular with the public. In fact he will pay that star many times more than an unknown whose acting talent is equal or even better than what the star offers. The unknown has no box-office drawing ability so he provides no real added value. The star however will bring in paying customers and he has a monopoly since there is only one of him. He has a high added value and can demand a lot of money to play the part.

Consider also professional sports. The National Basketball Association, the National Football League, and major league baseball have effective monopolies on their product. They could put franchises in any city big enough to support a top-notch team in their sport but they don't. Instead they limit the number of teams. They know that many cities regard having a major sports team as a very desirable status symbol so they make sure that there are fewer teams available than cities wanting those teams. That forces those cities to compete against each other. Typically the city must be willing to provide a fancy stadium or other facility. In many cases it is the city, not the team owner that foots the bill for that and is stuck with that bill should the team move to another city. Any given city has an added value of essentially zero when negotiating with a professional sports league. (There are some exceptions such as New York with so many potential fans that they want teams there. However even there the “New York” Giants and Jets actually play in New Jersey.)

That is one reason why professional teams often move to new cities. They get better deals by moving. The Seattle SuperSonics became the Oklahoma City Thunder. The St Louis Cardinals now play in Arizona. The Dodgers long ago stopped dodging trolley cars in Brooklyn and moved to Los Angles. Many other teams no longer play where they once did, leaving behind empty stadiums or arenas and unhappy fans and taxpayers. Cities are put in a position in which they cannot win in that game.

What should cities do to level the playing field with the sports leagues? Clearly bidding against each other is a losing battle; the team owners have all the power. They have only two rational choices. First of course they can just refuse to play the game, tell the sports team owner that they are not going to give him any special treatment. That is an option I think voters and taxpayers should insist on in the present situation. The other rational choice is to get together as a league of cities and negotiate as a group. Such a group would have an added value equal to that of the sports league. No longer would the owner of the Seattle Sonics be able to tell Seattle and Oklahoma City that they better give him what he wants or he will go to another city. That owner would have to deal with a league of cities that has as much added value as he does. Of course cities being jealous of one another will probably never form such a league so the owners will continue to have all the power.

I could go on but you get the point. Any person, city, or business that understands added value can use that concept to decide if it wants to play the game. If it does play, that concept helps know how to play and what results to expect.

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