Game Theory and Behavioral Evidence

In earlier sections, we reviewed some problems that arise from treating classical (non-evolutionary) game theory as a normative theory that tells people what they ought to do if they wish to be rational in strategic situations. The difficulty, as we saw, is that there seems to be no one solution concept we can unequivocally recommend for all situations, particularly where agents have private information. However, in the previous section we showed how appeal to evolutionary foundations sheds light on conditions under which utility functions that have been explicitly worked out can plausibly be applied to groups of people, leading to game-theoretic models with plausible and stable solutions. So far, however, we have not reviewed any actual empirical evidence from behavioral observations or experiments. Has game theory indeed helped empirical researchers make new discoveries about behavior (human or otherwise)? If so, what in general has the content of these discoveries been?

In addressing these questions, an immediate epistemological issue confronts us. There is no way of applying game theory ‘all by itself’, independently of other modelling technologies. Using terminology standard in the philosophy of science, one can test a game-theoretic model of a phenomenon only in tandem with ‘auxiliary assumptions’ about the phenomenon in question. At least, this follows if one is strict about treating game theory purely as mathematics, with no empirical content of its own. In one sense, a theory with no empirical content is never open to testing at all; one can only worry about whether the axioms on which the theory is based are mutually consistent. A mathematical theory can nevertheless be evaluated with respect to empirical usefulness. One kind of philosophical criticism that has sometimes been made of game theory, interpreted as a mathematical tool for modelling behavioral phenomena, is that its application always or usually requires resort to false, misleading or badly simplistic assumptions about those phenomena. We would expect this criticism to have different degrees of force in different contexts of application, as the auxiliary assumptions vary.

So matters turn out. There is no interesting domain in which applications of game theory have been completely uncontroversial. However, there has been generally easier consensus on how to use game theory (both classical and evolutionary) to understand non-human animal behavior than on how to deploy it for explanation and prediction of the strategic activities of people. Let us first briefly consider philosophical and methodological issues that have arisen around application of game theory in non-human biology, before devoting fuller attention to game-theoretic social science.

The least controversial game-theoretic modelling has applied the classical form of the theory to consideration of strategies by which non-human animals seek to acquire the basic resource relevant to their evolutionary tournament: opportunities to produce offspring that are themselves likely to reproduce. In order to thereby maximize their expected fitness, animals must find optimal trade-offs among various intermediate goods, such as nutrition, security from predation and ability to out-compete rivals for mates. Efficient trade-off points among these goods can often be estimated for particular species in particular environmental circumstances, and, on the basis of these estimations, both parametric and non-parametric equilibria can be derived. Models of this sort have an impressive track record in predicting and explaining independent empirical data on such strategic phenomena as competitive foraging, mate selection, nepotism, sibling rivalry,herding, collective anti-predator vigilance and signaling, reciprocal grooming, and interspecific mutuality (symbiosis). (For examples see Krebs and Davies 1984, Bell 1991, Dugatkin and Reeve 1998, Dukas 1998, and Noe, van Hoof and Hammerstein 2001.) On the other hand, as Hammerstein (2003) observes, reciprocity, and its exploitation and metaexploitation, are much more rarely seen in social non-human animals than game-theoretic modeling would lead us to anticipate. One explanation for this suggested by Hammerstein is that non-human animals typically have less ability to restrict their interaction partners than do people. Our discussion in the previous section of the importance of correlation for stabilizing game solutions lends theoretical support to this suggestion.

Why has classical game theory helped to predict non-human animal behavior more straightforwardly than it has done most human behavior? The answer is presumed to lie in different levels of complication amongst the relationships between auxiliary assumptions and phenomena. Ross (2005a) offers the following account. Utility-maximization and fitness-maximization problems are the domain of economics. Economic theory identifies the maximizing units — economic agents — with unchanging preference fields. Identification of whole biological individuals with such agents is more plausible the less cognitively sophisticated the organism. Thus insects (for example) are tailor-made for easy application of Revealed Preference Theory (see Section 2.1). As nervous systems become more complex, however, we encounter animals that learn. Learning can cause a sufficient degree of permanent modification in an animal's behavioral patterns that we can preserve the identification of the biological individual with a single agent across the modification only at the cost of explanatory emptiness (because assignments of utility functions become increasingly ad hoc). Furthermore, increasing complexity confounds simple modeling on a second dimension: cognitively sophisticated animals not only change their preferences over time, but are governed by distributed control processes that make them sites of competition among internal agents (Schelling 1980; Ainslie 1992, Ainslie 2001). Thus they are not straightforward economic agents even at a time. In setting out to model the behavior of people using any part of economic theory, including game theory, we must recognize that the relationship between any given person and an economic agent we construct for modeling purposes will always be more complicated than simple identity.

There is of course no sudden crossing point at which an animal becomes too cognitively sophisticated to be modeled as a single economic agent, and for all animals (including humans) there are contexts in which we can usefully ignore the synchronic dimension of complexity. However, we encounter a phase shift in modeling dynamics when we turn from asocial animals to non-eusocial social ones. (That is, animals that are social but that don't, like ants, bees, wasps, termites and naked mole rats, achieve cooperation thanks to fundamental changes in their population genetics that make individuals within groups into near clones. Main known instances are parrots, corvids, bats, rats, canines, hyenas, pigs, weasels, elephants, hyraxes, cetacians, and primates.) In their cases stabilization of internal control dynamics is partly located outside the individuals, at the level of group dynamics. With these creatures, modeling an individual as an economic agent, with a single comprehensive utility function, is a drastic idealization, which can only be done with the greatest methodological caution and attention to specific contextual factors relevant to the particular modeling exercise. Applications of game theory here can only be empirically adequate to the extent that the economic modeling is empirically adequate.

H. sapiens is the extreme case in this respect. Individual humans are socially controlled to a degree unknown in any other non-eusocial species. At the same time, their great cognitive plasticity allows them to vary significantly between cultures. People are thus the least straightforward economic agents among all organisms. (It might thus be thought ironic that they were taken, originally and for many years, to be the exemplary instances of economic agency.) We will consider the implications of this for applications of game theory below.

First, however, comments are in order concerning the empirical adequacy of evolutionary game theory to explain and predict distributions of strategic dispositions in populations of agents. Such modeling is applied both to animals as products of natural selection (Hofbauer and Sigmund 1998), and to non-eusocial social animals (but especially humans) as products of cultural selection (Young 1998). There are two main kinds of auxiliary assumptions one must justify, relative to a particular instance at hand, in constructing such applications. First, one must have grounds for confidence that the dispositions one seeks to explain are (either biological or cultural, as the case may be) adaptations — that is, dispositions that were selected and are maintained because of the way in which they promote their own fitness or the fitness of the wider system, rather than being accidents or structurally inevitable byproducts of other adaptations. (See Dennett 1995 for a general discussion of this issue.) Second, one must be able to set the modeling enterprise in the context of a justified set of assumptions about interrelationships among nested evolutionary processes on different time scales. (For example, in the case of a species with cultural dynamics, how does slow genetic evolution constrain fast cultural evolution? How does cultural evolution feed back into genetic evolution, if it feeds back at all? For a supremely lucid discussion of these issues, see Sterelny 2003.) Conflicting views over which such assumptions should be made about human evolution are the basis for lively current disputes in the evolutionary game-theoretic modeling of human behavioral dispositions and institutions. This is where issues in evolutionary game theory meet issues in the booming field of behavioral-experimental game theory. I will therefore first describe the second field before closing the present article by giving a sense of the controversies just alluded to, which now constitute the liveliest domain of philosophical argument in the foundations of game theory and its applications.

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