ABSTRACT

The publication of von Neumann and Morgenstern’s Theory of Games and Economic Behavior in 1944 was greeted enthusiastically by many who thought they saw in it a method of solving virtually all strategic problems (see, e.g., the review of von Neumann and Morgenstern’s book by Copeland, 1945). But, alas, game theory seldom provides clear and feasible solutions to practical problems of everyday life. There are three major reasons for this.

Persuasive formal solutions exist only for strictly competitive (two-person zero-sum) games, but real strategic interactions are seldom strictly competitive even when they involve only two decision makers.

Human beings have bounded rationality (March, 1986; Simon, 1957, 1976, 1978, 1985) and cannot be expected to solve any but the simplest games. Chess, for example, is a strictly competitive game, no more complex than many everyday strategic problems, and the minimax theorem tells us that it has a definite solution; but knowing this is of no help in actually playing the game or even in programming a computer to play it. The most powerful chess computers conduct minimax searches for the “best” moves according to certain very restricted criteria, although they evaluate many millions of positions for each move that they make, but this “brute force” approach enables them to “think” only a few moves ahead (Hsu, Anantharaman, Campbell, and Nowatzyk, 1990; Scientific American, 1981). The average number of legal moves in a chess position is about 30, and a game of chess involves about 40 moves from each player, therefore the number of possible chess games is in the region of 3080 or 10120, far more than the number of particles in the universe (estimated to be between 1078 and 1080), which means that no chess computer will ever be able to find the optimal strategy by brute force. A computer programmed to solve the game, even if it could analyse a billion positions per second, would still be calculating its first move after billions of years. The information-processing capacity of human beings is modest by comparison, and brute force calculation is out of the question in most positions, but in spite of this grandmasters play remarkably strongly using methods that are not well understood by cognitive psychologists.

Two characteristic features of everyday strategic interactions are, first, that the players often have incomplete information about the games that they are playing (Harsanyi and Selten, 1988, pp. 9–12), and second, that the rules and payoff functions of the games often change – and are deliberately changed by the players – while the interactions are in progress (Colman, 1975). An ingenious method has been devised for incorporating incomplete information into game theory at a formal level (Harsanyi, 1967, 1968a, 1968b), but the possibility of variable rules and payoff functions can be incorporated only at the price of vastly increased complexity, making the theory as a guide to practical action all the more vulnerable to (2).