This chapter has reconsidered several aspects of noncooperative game theory, beginning with subgame perfect equilibrium and the analysis of games in extensive form. First, the analysis of such games in terms of local optimization of behavior strategies returns only a subset of Nash equilibria and thus may not return correlated equilibria. Correlated equilibria presuppose contingent strategies in some cases.
Second, analysis of games in extensive form following Kuhn’s paper in Kuhn and Tucker (1953) and Selten (1975) assume perfect recall. However, for some purposes, imperfect recall may be a more productive assumption. Imperfect recall allows us to recover the neoclassical model of monopoly in a cooperative analysis, to treat the economic game as being (ideally) imbedded in a political game, and provides a characterization of “perfect” competition that is an alternative to the assumption of a continuum of traders.
Finally, there is a contrast of two concepts of rationality. “Ideal rationality” links rationality to strength of will. It seems that ideal rationality is characteristic of cooperative game theory and is the substantive difference that distinguishes cooperative game theory from noncooperative game theory. The rationality of Selten (1976) is perfect rationality. “Perfect rationality” links rationality to weakness of will. The example of intertemporal inconsistency shows that perfect rationality characterizes neoclassical economics as well as noncooperative game theory. A third concept of rationality is “sophisticated rationality,” which is consistent with the belief that the population includes both types with strong and with weak will. This belief leads toward a world very much like the world we seem to live in, a world not susceptible to analysis in terms either of perfect or of ideal rationality.
- 1. Recall that “corn economy” is a phrase in the British language, not the American, so that “corn” means “grain,” such as wheat or oats, depending on the country, rather than maize specifically. For this section “corn” is an abstract wage-good.
- 2. This wages fund assumption was perhaps one of the least persuasive of classical ideas, and the first to be abandoned, but contains an important true insight: if production takes time, it will be necessary for the people who do the work to eat while production takes place, and if the money wage is raised while there is no increase in the quantity of wage- goods available, inflation is the only result. This fact has reasserted itself in the context of industrialization in the twentieth century and as recently as the food crisis of the spring of 2008. The unique function of capitalists in the classical corn economy is to supply the wage-goods from their stock of accumulated wage-goods.