Mindful strategists
As one of the founding fathers of modern game theory, Oskar Morgenstern was interested in how theories about the world can conceivably influence the world. If, for instance, an economist predicts that the business cycle will turn towards growth, this may support that it will become true.
More theoretically speaking, self-supporting theories can become commonly known without undermining their own “predictions”. They are “absorbable” (see Morgenstern and Schwodiauer 1976; Dacey 1976; Morgenstern 1972).Absorbability of a theory is a surprisingly strong requirement. To see why, imagine the most simple case of the classical “2 ? 2” battle of the sexes (Table 4).
For instance, a “theory” of rational play that recommends that players should be heading for the option that may lead to the best possible result for them is not absorbable. According to such a theory’s advice “He” should go to watch boxing and “She” should watch the film, but if the theory advice becomes known, both have good reason to deviate from it. That is, it cannot become commonly known that the “theory” implying the advice of “going for the best” is guiding actors without providing actors with reasons to deviate from the theory’s guidance.
Although von Neumann and Morgenstern did not explicitly use the concept of a Cournot-Nash equilibrium, its central role was implied by their “reasoning about knowledge” approach to interactive-decision making (see Buchanan et al. 2001; Fagin et al. 1995; and for a comparison with homoeostatic classical conceptions of equilibrium, Walsh and Gram 1980). Their view had the advantage of giving a clear reason why “equilibria” are important: A theory recommending some sort of play as rational must pick equilibria if the type of rationality embodied in the theory is to become common knowledge and operative among the actors whose behaviour is captured and guided by the theory (see for this in a bounded rationality context, Guth and Kliemt 2004).
To the extent that the theory is meant to be presenting the “decision logic” rather than the “decision psychology” of choice, absorbability is the central coherence criterion. A Cournot-Nash equilibrium is present only if the interaction “generates messages which do not cause agents to change the theories which they hold or the policies which they pursue” (Hahn 1973: 59) However, this is not sufficient for deriving clear action guiding advice from the theory. In the standard fully symmetric 2 ? 2 battle of the sexes game of Table 4, alternative theories, each suggesting a different equilibrium, could conceivably be absorbable.
For instance, a theory that would recommend the strategy combination leading to the result that the female player prefers most could as a matter of fact become common knowledge and could be observed by minimally rational individuals in view of their own payoffs. Yet, in this case, a theory is singled out by some contingent historical circumstance. It applies only to 2 ? 2 games in which female players are present. It would not be universally applicable - not even to all 2 ? 2 interactions. It cannot be commonly known rationality or decision logic per se that favour one theory of rational play over the other. An empirical fact is decisive where reason alone is insufficient.
As the preceding simple example already shows, there is no way to resolve strategic uncertainty in terms of rationality and reasoning alone. Common knowledge of rationality cannot serve as a sufficient “correlating signal” (see Aumann 1987). Some extra- rational clue - rendering one of the possible theories “focal” - is needed to coordinate successfully on a single equilibrium (see Sugden 1991, for this critique of Harsanyi and Selten 1988)).
To put it slightly differently, those who intend to engage the challenge of constructing theories only under the constraints of consistency and absorbability will not be able to solve the equilibrium selection problem “more geometrico”. Even what is rational is in some sense contingent and dependent on something in the real world that cannot be inferred by reason alone but requires knowledge of facts that typically emerge in a “path dependent”, contingent way from human practices. If mindful strategists cannot be guided by their reason alone, would a theory about mindless strategists (see Gul and Pesendorfer 2008) do any better?