Rationality of strategists
The anti-speculative climate of the interwar period of the last century was quite hospitable to the Hobbesian focus on expected (observable) consequences of action. Within the broadly behaviourist framework of the time it appeared as a great achievement that economists could show that, independently of any intention to maximize, individual behaviour can be described “as if” maximizing a utility function.
Provided that certain consistency and continuity axioms are fulfilled, an increasing function (monotone on the underlying implied ordering of the set on which it is defined) will summarily describe the choice-making of an actor who is rational in the sense of the axioms. In short, on sets of potential choices the function represents a rational individual’s choice-behaviour. From any feasible set the individual will choose an alternative to which maximal utility is assigned. However, this choice takes place without the utility value of the function being among the reasons for making it.Although the preceding characterization of “representative utility” is a banality, it is still frequently mixed up with (classical) “motivating utility”. To prevent confusion, the absolutely central concept of modern representative utility deserves to be spelled out somewhat more formally: If for two choices, A, B, the (order representing) utility function u(.) assigns values such that the relation u(A) < u(B) applies then this indicates that, whenever both A, B are present in a set of behavioural alternatives, A is not chosen from that set. The behaviour B is not shown because u(B) is greater than u(A). It is just the other way around. The expression u(B) > u(A) is simply shorthand to inform about “predicted” choice behaviour. Yet it does not provide a reason or an explanation for that behaviour in terms of motives. In particular, modern utility u is not a measure of, say, pleasure or satisfaction.
Maximization of u can be diagnosed from an external point of view but there is no motive, selfish or other, concerning “u” involved. Overt choice behaviour is only “as if” maximizing u but not brought about by an intention to maximize.The representation of choice behaviour by a (representative) utility function was extended to choices among lotteries and many powerful representation theorems for risky choices could be proven (see, for example, von Neumann and Morgenstern 1944; Savage 1954). Expected value formation - that is, “linear” probability weighting - on the basis of utilities representing risk attitudes is viable without distorting the representation of choices among lotteries. Risk is included from the beginning by using a basic reference lottery ticket (BRLT), (see Raiffa 1968, on such BRLT) instead of the measuring rod of (risk-free) money to assign order-representing numbers.
Owing to the representation theorems the formal apparatus of expected value formation and “maximization under constraints” remains intact under the re-interpretation of the concept of “utility”. The maximization under constraints approach of economists is not anymore restricted to those aspects of behaviour that are brought about by selfish pecuniary motives under the assumption of risk-neutrality. Provided that they fulfil certain consistency and continuity axioms, arbitrary motives and attitudes to risk can be represented such that behaviour can be described as if maximizing an expected value function “linear in probability”. However, for valid explanations of real choice-making “as if” is not good enough. For empirical explanations some kind of causal rather than logical “if-then” is required.
If nomological regularities of motivational processes are used to explain choicemaking, reliance on psychology seems unavoidable. Yet neo-classical economists try to avoid this by almost all means. Most of them resent any move away from homo oeconomicus or “rational expecting maximizing man” (see Meckling 1976) towards truly empirical science. This move is indeed subversive for their desire to derive insights “more geometrico” according to a “logic” - rather than a “psychology” - of action. Economists take to either “eductive” (mindful) or to “evolutionary” (mindless) game theoretically inspired a priori models (see, in particular, Binmore 1987, 1988).
Table 4 Battle of the sexes
| She He | Boxing | Cinema |
| Boxing | (2, 1) | (0, 0) |
| Cinema | (0, 0) | (1,2) |