Could the backward induction controversy be a metaphorical problem?

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The backward induction controversy in game theory emerged and practically ended in the 1990s. The protagonists however did not converge to an agreement for explaining the controversy. Why is this the case if opposing sides had access to the same modeling techniques and empirical facts? In this paper I offer an explanation to this controversy and to its unsettled end. It is argued that the answer is not to be found in the modeling claims made by the opposing protagonists but in the tacit metaphors they operate under. Metaphor in Greek means the transfer of meaning from one domain to another. Aristotle defines metaphor as giving a “thing a name that belongs to something else” (Poetica 1457b). The meaning of metaphors has not changed much since then in contrast to models which are comparatively new and still not well understood modes of scientific reasoning. Metaphors provide an independent standard of evaluation from models. The aim of this paper is to utilize game theory to provide a case study that illustrates how modeling, by itself, is not sufficient to overcome the controversies it generates. Metaphor, as a distinct mode of reasoning, could however successfully explain them. The controversy of backward induction in game theory in particular can be used as testing ground for this hypothesis. The paper frames the controversy in terms of metaphor choice to provide a common qualitative reasoning framework to those involved in it. This results in the identification of three different domains—mathematical logic, game theory, and the economic world–each connected to the other via different metaphors. The controversy on backward induction is placed in, and tentatively explained by, this framework.

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