Competition and Cooperation by Roger A. McCain

One of the most prominent facts about game theory is that there is not one game theory but two: cooperative and noncooperative game theory. In cooperative game theory we assume that whenever there is a possibility for agents to create some mutual benefit by choosing a common strategy, rational agents will realize that possibility. In noncooperative game theory we assume that a rational agent attempts to anticipate the strategy choices of others and choose a best response to them. This independent choice of strategies may leave possibilities for mutual benefit unrealized. When John Nash introduced the distinction, he was influenced by his undergraduate study of economics. But economics traditionally is organized around a different, overlapping dichotomy: competition versus monopoly, Roger McCain goes on to explain.

We find this dichotomy of competition and monopoly in its clearest form in the words of John Stuart Mill “wherever competition is not, monopoly is; and … monopoly, in all its forms, is the taxation of the industrious for the support of indolence, if not of plunder.” More recent economists, who would be surprised to learn that they have been influenced by Mill, retain his dichotomy and his judgments on the two sides of it. We speak of “imperfect competition,” in which competition is not strong enough to offset all elements of monopoly. Our controversies are about just how imperfect competition is, and what, if anything, public policy ought to do about it.

But there was always a “cooperative” aspect of “competition.” Exchange is a form of cooperation. This was a key idea of the “neoclassical revolution:” the classical cost theory of value was replaced by a subjective value theory that recognized that exchange could result in mutual benefit, a surplus. But how is the surplus shared out between the parties to the exchange? That depends on the terms of exchange, the price. Marshall resolved this circularity by supposing that the price is determined by the competitive process. The surplus is then divided between consumers’ surplus and producers’ surplus.

It is here that competition is tied to noncooperation. Each competitor chooses her best response to the price, which is a consequence of the strategy choices of all other agents, along with her own. In the jargon of economics, we say that she treats the market price as a parameter in deciding how much to buy or sell. In the jargon of game theory, we say that she has a “dominant strategy,” in that she needs not know the strategy choices of the others in any detail in order to choose her own best response. Thus the competitive theory is a theory of cooperative exchange that takes place on terms that are determined noncooperatively.

The real world we live in seems to be a mixture of cooperative and noncooperative activities, and the competitive theory speaks to that. If we lived in a world of self-employed individuals and their individual customers, we might stop there. But what about the business firm? If we return to Adam Smith and his example of the pin factory, we see a different vision of the business firm: one in which the firm coordinates division of labor – which is to say that those associated in the firm choose a common strategy for their mutual benefit. What about common property resources, and the “tragedy of the commons?” Here we see that noncooperative, but competitive, decisions lead to overexploitation and inefficiency.

Here, we shall focus on the business firm, with employees anywhere in the range from a few to thousands. Modern economics treats this not as an organization but as a bundle of bilateral contracts of exchange – exchange of labor for money in some cases, and exchange of commodities or services for money in other cases – with the terms of the exchange, in each case, determined by a noncooperative equilibrium of some sort. These bundles of bilateral exchanges, these business firms, have been described as “islands of conscious power in this ocean of unconscious cooperation like lumps of butter coagulating in a pail of buttermilk,” but they might better be called lumps of multilateral cooperation in an ocean of noncooperation. In a very few cases, the business firm has been studied as a cooperative coalition among employees and employers. In Game Theory and Public Policy, Cch 11-14, McCain explores the firm as a coalition among employees, employers, and customers. Some of the traditional learning about profit maximization can apply, since rational agents will maximize the surplus they divide among themselves. On the other hand, the cooperative perspective tells us that the distinction between insiders and outsiders is unavoidable – not a product of inflexible labor laws but of the limits on cooperation.

But what are those limits, and why? To be fair, cooperative game theory is mostly quite abstract. A central principle of cooperative game theory is that coalition surpluses are superadditive; that is, whenever we merge two coalitions, the surplus that can be produced by the merged coalition is no less than the sum of the surpluses they had produced separately, and in general more. Why, then, do we see these lumps of cooperation in a sea of noncooperation? Why does the butter not absorb all of the buttermilk? The answer is that cooperative decision-making is costly. It requires a great deal of information, and information is not free. For production and sales, cooperation requires sharing of information. Thus, cooperation for production can take place only among those who are linked in appropriate ways, with links of information sharing. These links must be created, again at some cost. Some of the activities that tend to create those links are known as job search and matching, marketing, and shopping. Thanks to Nobel laureate research in the last generation, we have learned a great deal about job search and matching, and their impacts on labor markets and the macroeconomy. The broader view – the firm as a coalition limited by links of information sharing in general – remains largely unexplored territory.

Roger A. McCain is  Professor at the School of Economics, LeBow College of Business, Drexel University, USA.

The first chapter of Roger’s second edition of Game Theory and Public Policy can be downloaded for free on Elgaronline.