Game-theoretical Concepts in Economics

In discussing applications of game theory, Shubik (1982) points out a major misconception. Maximin strategies and the saddlepoint solution are assumed to be central to the game-theoretic analysis of multi-person decision making. The source of this misconception is easy to see. The theory of games grew out of a rigorous analysis of so-called parlour games (e.g., chess, poker). In contrast to games associated with sports, where physical prowess and flexibility are often crucial, the decisive factor in parlour games is strategic acumen. Indeed, these games are often called games of strategy. Moreover ‘winning’ (as opposed to losing) is usually a principal motivation in playing these games. Thus, the two-person constant sum game represents the best known type of game of strategy. It is also the starting point in the development of game theory. Indeed 6 of the 12 chapters of von Neumann and Morgenstern’s fundamental treatise (1947) are devoted to zero sum games. Of these, two chapters deal with the two-person zero sum game, in which the interests of the players are diametrically opposed. The other four deal with zero sum games with more than two players. The players, however, are supposed to split into two coalitions with diametrically opposed interests. In this way, the theory is partly ‘reduced to the preceding case’ a method of theory building to which the mathematician frequently resorts.