Abstract
Game theory is a formal approach to behavior that focuses on the strategic aspect of situations. The game theoretic approach originates in economics but has been embraced by scholars across disciplines, including many philosophers and biologists. This approach has an important weakness: the strategic aspect of a situation, which is its defining quality in game theory, is often not its most salient quality in human (or animal) cognition. Evidence from a wide range of experiments highlights this shortcoming. Previous theoretical and empirical work has sought to address this weakness by considering learning across an ensemble of multiple games simultaneously. Here we extend this framework, incorporating artificial neural networks, to allow for an investigation of the interaction between the perceptual and functional similarity of the games composing the larger ensemble. Using this framework, we conduct a theoretical investigation of a population that encounters both stag hunts and prisoner’s dilemmas, two situations that are strategically different but which may or may not be perceptually similar.
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Notes
These assumptions are also relaxed by the consideration of games of incomplete information, which we will discuss later.
The choice of 10 features is a balance between a desire for gradations in perceptual similarity, requiring more features, and a desire for agents with smaller neural networks and hence less computational cost for simulations. Although binary and real valued features are both compatible with artificial neural networks, we have chosen binary perceptual features here as they are readily interpretable either at the lowest sensory level as the spiking of a single sensory neuron, or at a more complex cognitive level as the presence or absence of some learned perceptual feature. Such high level features might be, for example, whether a green light is on, whether a con-specific is present, or whether someone has mentioned the word risk in recent conversation.
The selection of this cooling regime is critical to the results of these simulations. This particular regime was chosen as roughly the quickest cool-down that still allowed for some discrimination in the case where perceptual similarity as created by method 3 and where there are an equal number of stag hunts and prisoner’s dilemmas in the environment. A quicker cooling rate entails less exploration and hence less discrimination, whereas a slower cooling rate entails more exploration and hence more discrimination. The particular choice of cooling regime is unimportant for the demonstration of our point that perceptual similarity is important in determining the outcomes of learning in a multi game environments.
The intermediate level of cooperation observed when 0.3 of the games encountered are prisoner’s dilemmas is the result of the population converging on always cooperating in some simulations, and converging on always cooperating in other simulations. This is to be expected. When 0.3 of the games encountered are prisoner’s dilemmas and initially the population plays cooperate and defect with equal probability, the expected value of playing cooperate and defect are very close, 1.5 and 1.45 respectively, making these particular simulations very sensitive to initial stochasticity.
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Acknowledgments
All authors gratefully acknowledge the support of the Swedish Research Council, grants 2009-2390 and 2009-2678, and the constructive comments of four anonymous reviewers. DC is also grateful for support from the John Templeton Foundation.
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Cownden, D., Eriksson, K. & Strimling, P. The implications of learning across perceptually and strategically distinct situations. Synthese 195, 511–528 (2018). https://doi.org/10.1007/s11229-014-0641-9
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DOI: https://doi.org/10.1007/s11229-014-0641-9