A Basic Cooperative Game

It's not very hard to find an example of a cooperative solution to game. In fact, we have been talking about cooperative solutions all through this course. Buying and selling is a cooperative game in which the buyer and the seller are the two "players" and the price they agree upon is their common strategy. Here's a numerical example to illustrate what I mean.

We suppose that Joey has a bicycle. Joey would rather have a game machine than a bicycle, and he could buy a game machine for $80, but Joey doesn't have any money. We express this by saying that Joey values his bicycle at $80. Mikey has $100 and no bicycle, and would rather have a bicycle than anything else he can buy for $100. We express this by saying that Mikey values a bicycle at $100.

The strategies available to Joey and Mikey are to give or to keep. That is, Joey can give his bicycle to Mikey or keep it, and Mikey can give some of this money to Joey or keep it all. It is suggested that Mikey give Joey $90 and that Joey give Mikey the bicycle. This is what we call "exchange." Here are the payoffs:

EXPLANATION: At the upper left, Mikey has a bicycle he values at $100, plus $10 extra, while Joey has a game machine he values at $80, plus an extra $10. At the lower left, Mikey has the bicycle he values at $100, plus $100 extra. At the upper left, Joey has a game machine and a bike, each of which he values at $80, plus $10 extra, and Mikey is left with only $10. At the lower right, they simply have what they begin with -- Mikey $100 and Joey a bike.

If we think of this as a noncooperative game, it is much like a Prisoners' Dilemma. To keep is a dominant strategy and keep, keep is a dominant strategy equilibrium. However, give, give makes both better off. Being children, they may distrust one another and fail to make the exchange that will make them better off. But market societies have a range of institutions that allow adults to commit themselves to mutually beneficial transactions. Thus, we would expect a cooperative solution, and we suspect that it would be the one in the upper left.

Thus, we can see that cooperative solutions are not uncommon in a market society. On the contrary! They are the essence of a market system! Thus, we cannot rule out the possibility that oligopolists will arrive at a cooperative solution, and charge a monopoly price and get monopoly profits.