How Models Fail
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Axelrod himself was confident that simulation studies like his yield knowledge that can be applied in the context of empirical application. In his book “The Evolution of Cooperation” (Axelrod 1984) he provided two case studies. One of these concerned biology. It was of highly speculative character as Axelrod honestly admitted and it has indeed never been confirmed since. Therefore, I am not going to discuss this particular case study here. Further biological research on the evolution of cooperation will briefly be outlined below.
The other one of Axelrod's case studies was a highly dramatic case study concerning the Live and Let Live System which emerged on some stretches of the deadlocked western front between enemy soldiers in World War One. However, as acknowledged by Axelrod his case study relies entirely on the prior historiographic work by Tony Ashworth (1980). Based on an extensive study of the historical sources, Ashworth had crafted a careful and highly differentiated explanation for the emergence, sustainment and eventual breakdown of the Live and Let Live on the western front. Axelrod's recasting of this story in game theoretical terms has nothing to add in terms of explanatory power, because the RPD-model is far too simple to account for the complicated network of causes for the Live and Let Live that Ashworth study had revealed (Arnold 2008, 180ff.). Even among game theorists it was disputed, whether there existed any straight-forward way to interpret the situation as a Prisoner's Dilemma at all (Schuessler 1990, 33ff.). Thus, if any particular scientific approach is to be credited with the successful explanation of the Live and Let Live in World War One, then it is not game theoretical modeling or computer simulations but the well-established methods of traditional historiography. Interestingly, though, this dramatic case-study did a lot to increase the popularity of Axelrod's simulation approach.
If Axelrod's attempts to apply his model to empirical case studies weren't particularly successful, then subsequent research could still demonstrate that the empirical application of these models is possible. The most noteworthy attempt to apply the RPD empirically was undertaken by Manfred Milinski (1987), who sought to explain the seemingly cooperative behavior that shoal fishes show when inspecting a predator. This paper is quoted time and again when it comes to giving an example for the empirical applicability of the RPD model. For example, Hoffman maintains in a research report about Axelrod's RPD framework that “This general framework is applicable to a host of realistic scenarios both in the social and natural worlds (e.g. Milinski 1987).” (Hoffmann 2000, 4.3). Milinski's 1987-paper, however, remains the sole example for the “host of realistic scenarios” to which this framework is supposedly applicable. The same paper by Milinski is quoted in Osborne's “Introduction to Game Theory” as an example for the empirical applicability of game theory (Osborne 2004, 445). Unfortunately, it was already by the late 1990s clear that Milinski's explanation of the predator inspection behavior did not work (Dugatkin 1997, Dugatkin 1998a). The reason is that it is not possible to obtain the necessary empirical data to either confirm or disconfirm the RPD model in the case of the predator inspection behavior of sticklebacks. This is also more or less the conclusion at which Milinski and Parker arrive in a joint paper on the same topic that they published 10 years after the initial study by Milinski (Milinski/Parker 1997, 1245).
In a broad meta-study on the research on “Cooperation among Animals” Lee Allan Dugatkin (1997) does not find a single instance of animal cooperation where any of the many variants of the RPD model (Dugatkin lists more than two dozens of them in the beginning of his study) can successfully be applied. He summarizes the situation in a very thoughtful article as follows: “Despite the fact that game theory has a long standing tradition in the social sciences, and was incorporated in behavioral ecology 20 years ago, controlled tests of game theory models of cooperation are still relatively rare. It might be argued that this is not the fault of the empiricists, but rather due to the fact that much of the theory developed is unconnected to natural systems and thus may be mathematically intriguing but biologically meaningless” (Dugatkin 1998, 57). The same frustration about empirically ungrounded model research is expressed by Peter Hammerstein: “Why is there such a discrepancy between theory and facts? A look at the best known examples of reciprocity shows that simple models of repeated games do not properly reflect the natural circumstances under which evolution takes place. Most repeated animal interactions do not even correspond to repeated games.” (Hammerstein 2003, 83). It is safe to say that there exist no successful empirical application cases for the RPD in biology. But the fact that the modeling community still entertains the believe that there are such successful application cases, if not “a host of” them, clearly demonstrates how little, in fact, the community occupies itself with empirical matters.
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