by From Bernard Guerrien One of the most widespread myths in economics, but also in sociology and political science, is that game theory provides “tools” that can help solve concrete problems in these branches – especially in economics. Introductory and advanced textbooks thus often speak of the “applications” of game theory that are being made, giving the impression that they are revolutionizing the social sciences. But, looking more closely, we see that the few examples given concern mostly the usual “stories” (prisoners’ dilemma, “chiken”, battle of sexes, entry deterrence, store chain paradox, centipede game, etc.) of “old” game theory. Take the four volume set Handbook of Game Theory with Economic Applications – a Handbook that provides an extensive account of what has been done in
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from Bernard Guerrien
One of the most widespread myths in economics, but also in sociology and political science, is that game theory provides “tools” that can help solve concrete problems in these branches – especially in economics. Introductory and advanced textbooks thus often speak of the “applications” of game theory that are being made, giving the impression that they are revolutionizing the social sciences. But, looking more closely, we see that the few examples given concern mostly the usual “stories” (prisoners’ dilemma, “chiken”, battle of sexes, entry deterrence, store chain paradox, centipede game, etc.) of “old” game theory. Take the four volume set Handbook of Game Theory with Economic Applications – a Handbook that provides an extensive account of what has been done in the field of game theory from its beginning, especially in economics, but not exclusively. Despite its title, there is not the slightest trace of a concrete example of an application, nor do we find any numerical data in its thousands of pages. This is not surprising. Mathematical reasoning requires clear and explicit enunciation of the assumptions used in its demonstrations. In particular, the assumptions concerning the information available to each player – his payoffs and those of the other players for each outcome of the game, the rules of the game, etc. – are so restrictive that there is no concrete situation in the world where they could possibly be verified, not even roughly (Guerrien, 2004, p. 2-3). As Ariel Rubinstein, another renowned game theorist puts it:
“Nearly every book on game theory begins with the sentence: ‘Game theory is relevant to …’ and is followed by an endless list of fields, such as nuclear strategy, financial markets, the world of butterflies and flowers, and intimate situations between men and women. Articles citing game theory as a source for resolving the world’s problems are frequently published in the daily press. But after nearly forty years of engaging in this field, I have yet to find even a single application of game theory in my daily life” (Rubinstein, 2013, my italics).
Most serious game theorists know this but they are reluctant to admit it[1]. In his recent overview of the subject “Game Theory in Economics and Beyond”, published in the Journal of Economic Perspective, Larry Samuelson, a prominent game theory specialist, gives a typical example of this contradictory [schizophrenic] attitude. Though it was probably not his intention, Larry Samuelson’s paper gives us a good picture of the impasse that game theory is in. After telling us that the theory, and its “tools” have become “essential”, – notably in economics where it leads to “extraordinarily useful models” –, the description that he gives of the state that the theory is in contradicts this rosy characterization. This is the case, for example, when he calls the mass of “refinements” of Nash equilibrium as “a menagerie”.
He is even less satisfied with the so-called “evolutionary” game theory, a branch that was “surrounded by a great deal of excitement” in the 1990s and has since “receded into the background.”
Apart from this contradictory attitude, Larry Samuelson, like many of the other prominent game theorists, makes some elementary logical mistakes. A typical example concerns his mischaracterization of Cournot’s model “solution” (equilibrium).
[1] David Kreps also expresses skepticism, but less clearly than Ariel Rubinstein.
Bernard Guerrien “On the current state of game theory”,
real-world economics review, issue no. 83, 20 March 2018, pp. 35-44, http://www.paecon.net/PAEReview/issue83/Guerrien83.pdf