Ashton Sperry

Game theory is the mathematical analysis of social systems. The sciences use game theoretic models as highly idealized explanations of social systems through equilibrium states. Call these explanations ‘equilibrium explanations’. They remove all causal information and dynamics to reveal deeper, underlying structural relationships. The hope is that removing causal information makes equilibrium explanations valuable and powerful, to the point that they explain better than their causal counterparts, despite being highly idealized.

However, I argue that equilibrium explanations, as currently ideated, are poor explanations of social systems. I identify three features about equilibrium explanations: (1) Equilibrium explanations must consider multiple, competing equilibria when explaining social systems; (2) causal information demarcates between equilibria, establishing equilibrium explanations as causal explanations; and (3) the value and power of equilibrium explanations increases proportionally to the amount of causal information provided by the parent sciences (e.g., anthropology, biology, economics, etc.), to the point that equilibrium states become irrelevant to explaining social systems. The result is that the sciences should reevaluate the explanatory power of equilibrium explanations.

Consider the example of evolutionary explanations of social norms. Game theorists traditionally model the emergence of social norms through a system of differential equations to provide a “top-down” equilibrium analysis. The benefit is that these models are mathematically tractable and can be solved analytically. However, they are very simple and idealized.

I instead advocate agent-based models of social norms. Individual agents are programmed with their own objectives, instead of using differential equations to represent the state of the whole system. Agent-based models provide at least two levels of analysis. One, a scientist can study the dynamics of the whole system based on the actions of individual agents. Two, a scientist can study the dynamics of individual agents based on the changes of the whole system. Agents are unique in their characteristics and only interact with some and not others depending on location and time. This approach allows scientists to study the complete interaction of numerous agents who are different from each other in specific ways.  Radically different social norms emerge depending on the range of the type of agents included in the model. This approach allows for studying specificcausal mechanisms behind converging behavior, and why agents switch from one equilibrium to another, or to none at all.

The range of these causal mechanisms greatly affects a population’s equilibrium state. Change the causal mechanisms, and different behaviors result. It is reasonable to refine said causal mechanisms to more accurately model further distinctions in behavior, creating specific causal histories to empirically investigate. This allows for the empirical accuracy of a model’s causal mechanisms to increase in importance when refining the models for greater explanatory power. The parent sciences (e.g., anthropology, biology, economics, etc.) are important. Indeed, when explaining the social norms of particular cultures, appealing to equilibrium explanations do not provide any additional information beyond the explanations of the parent sciences. Interestingly, equilibrium explanations in this context are not relevant to explaining the occurrence of particular social norms, due to the requirement for causal information.

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