In dealing with Aumann, like Friedman, we turn to the epistemic views on an area of science held by one of its accepted authorities. Aumann is an expert in Game Theory
Aumann rejects the "man in the street" idea of science as aiming at practical applications (solving practical problems, yielding new possibilties, like technical improvements and strategies to improve health, happiness etc.). Aumann considers as "more sophisticated observers" those who use predictive power as a criterion for what is scientific and what isn't, but he disagrees with them too. This clearly distinguishes him from Friedman. Aumann's basic criterion is set in terms of understanding, or comprehension. Applied to game theory it is the ability to unify an aspect of rationality in interactive decision making.
"Truth" is not the aim of game theory. Observations can be judged for truth, not theories. This means there may be many different "good" theories about the same set of observations, which is the fact in game theory (that is called pluralism). The distinction between theories and observations is not always clear: theories might mature to observations, and, conversely, a more developed view might turn some "observation" into a "bad theory".
He adresses the notorious task to defend the scientific status of the utility maximization postulate. Many economist -Lionell Robbins and Ludwig von Mises are protagonists here- do so by pointing at its obvious rationality. Friedman opposed this and considered its plausibility to be irrelevant. He claimed that the postulate should be judged on its power to yield correct predictions about the "phenomena the theory is designed to explain". Aumann accepts neither: "...the validity of utility maximization...derives from its being the underlying postulate that pulls together most of economic theory; it is the major component of a certain way of thinking, with many important and familiar implications, which have been part of economics for decades and even centuries".
Game theory could be seen as a descriptive, normative or as a classifying science (and more, which we shall not treat here).
As a descriptive science game theory, Aumann holds in accordance with J.S.Mill, describes rational behaviour only. That makes game theory unlike physics or astronomy. Often people do not act fully rational and the resulting game will not conform its game theoretic model. "Descriptively speaking,then, we can expect our disciplines only sometimes to explain or provide insights into 'real' phenomena. We cannot expect them always to do so, because they are admittedly incomplete. We cannot even say beforehand when we expect them to do so, because we do not yet know how to integrate rational sciences like game theory and economics with non-rational sciences like psychology and sociology to yield accurate predictions. The criterion for judging our theories cannot be rigid; we cannot ask, is it right or is it wrong? Rather, we must ask, how often has it been useful? how useful has it been? All this may sound very slippery and unsatisfactory. There are no firm predictions, no falsifiability. If our theory appears not to work, we don't loose any sleep. 'Rationality is just one of the relevant factors', we say blandly; 'here something else was at work.' (Aumann (1985), 36-37)"
As a normative science the advice to players might seem so simple as telling them to behave according to the rationality assumptions attributed to them in the game theoretic model. But this holds only if the advice is to all players. The descriptive problem is creeping back in as soon is the advice is to part of the players only: will the rationality assumption be correct for the other players, considered exogenous?
Exercize: In the mid-nineteenth century a man in Paris was arrested who made a living of predicting the sex of unborn babies, refunding the fee in case of error. And refunding he did faithfully! Question 1: is this man rational? Why (not)? Question 2: are his clients rational? Why (not)? Question 3: is it rational to have this man arrested? Why (not)?
The classifying function of game theory makes you aware of the difference between cooperative and non-cooperative games, games with complete and incomplete information. In general, by considering models, even ones that are too abstract to have any practical application, one may find that some are of different types, and some that might seem of different type at first sight, seem similar on deeper analysis.
One of the most important metatheoretical concepts of game theory is that of a solution. The solution of a game is the set of decisions made by all players and the resulting pay offs of all players. What will be the solution depends on the solution concept used by the game theorist. There are many such concepts, such as the Nash equilibrium, the "core", the von Neumann-Morgenstern stable set and the N-M stable set. Aumann: "Game-theoretic solution concepts should be understood in terms of their applications, and should be judged by the quantity and quality of their applications. The solution concepts we have considered all have different kinds of applications, which reflect back on the solution concepts and yield different interpretations of them. In each case, important descriptive and normative insights result; each of the concepts unifies a different aspect of rationality in interactive decision making.
Literature:
Aumann, Robert J. (1985) "What is Game Theory Trying to Accomplish?", in: Arrow, K. and S. Honkapohja (eds) Frontiers of Economics, Oxford, Basil Blackwell.
"On the State of the Art in Game Theory: An Interview with Robert Aumann"
Interview by Eric van Damme in: W. Albers, W. Gueth,P.Hammerstein,B. Moldovanu, E.
van Damme (eds): Understanding strategic interaction: essays in honor of Reinhard Selten,
Springer 1996.