# RATIONALITY

The contrast has been noted again and again between contingent strategies underlying cooperative game theory and the behavior strategy often applied in noncooperative game theory; and so also has the contrast between cooperative and noncooperative game theory in general. In this section the argument will be made that these differences are at base different conceptions of rationality. The issue is *not* whether people are rational, irrational or partly irrational. Rather, the issue is what it means to say that people are rational, either wholly or partly.

## Weakness of Will and Rationality

Noncooperative game theory has been greatly influenced by Selten, and his 1975 paper is a key paper for our purposes here. It is interesting to contrast the assumptions of this paper with Selten’s earlier view (1964). There, we recall, Selten had acknowledged in an afterword that his (cooperative) model in the 1964 paper required the assumption that players could commit themselves to any contingent pure strategy, acknowledging Thomas Schelling (1960) as the source of his change of mind. In 1975 Selten’s assumptions are reverse to those he made in 1964, but his terminology is also inconsistent in a way that may obscure the difference. Selten defines a pure strategy not as a plan assigning probability 1 to one of all possible contingency plans, as von Neumann and Morgenstern did and as Selten did in 1964, but as the assignment of probability 1 to a particular behavior strategy choice at a particular information set. Selten now assumes what Schelling (1980) called weakness of will.

But this will make no difference for rational behavior as Selten now conceives it. Selten limits his subject matter to games with perfect recall. He writes (1975 p. 320): “Since game theory is concerned with the behavior of absolutely rational decision makers whose capabilities of reasoning and memorizing are unlimited, a game, where the players are individuals rather than teams, must have perfect recall.” He then excludes consideration of teams, and he justifies this by limiting his scope to “strictly noncooperative games.” This means Kuhn’s multiple-agent games are excluded. For multiple agents to be joined together as a single player would require a cooperative agreement among them, and this is excluded by assumption. But this, taken with Selten (1975 p. 328): “Player 2’s choices should not be guided by his payoff expectations in the whole game but by his conditional payoff expectations,” tells us that for rational behavior as Selten now conceives it, there can be no commitment whatever. By assumption, only behavior strategies are relevant to rational behavior.

This concept of rationality has become predominant in economics as well as noncooperative game theory, and it is appropriate now to expand on the different concepts of rationality in those fields and in most cooperative game theory.

In economics, the issue of weakness of will and commitment arises in the context of intertemporal inconsistency of rational choice (Strotz, 1956). We adopt the neoclassical convention of expressing time preference by a discount rate. Most economic literature assumes that this discount rate per unit time is the same regardless of the delay before the payment is made. This assumption of a uniform rate of time preference has no basis in empirical observation, but is made in order to reconcile the theory of rational choice, as it is understood in modern economics, with the assumption of time preference. The difficulty is that a non-constant rate of discount can result in what are called intertemporal inconsistencies in decision making. What this means is that a rational, maximizing decision maker would make one decision at one point of time, but at a later point of time would rationally prefer the alternative he has initially, rationally rejected. (There has been some recent research on alternatives to constant rates of time preference, such as hyperbolic discounting, but it has been directed to a different issue.)