Models of Mechanisms: The Case of the Replicator Dynamics - Mechanism and Causality in Biology and Economics - page 83

Prima facie, the abstract mechanisms account fits well with observed scientific
practice. Scientists often speak about abstract causal structures as if they were real.
They see patterns, structures and processes instantiated in various events that
produce phenomena: for example, natural selection in the genesis of traits of
many different organisms or positive feedback loops yielding dominance of certain
set-ups in many institutions. They model these abstract patterns, structures and
processes and suggest that these models represent something real.
Conversely, scientists sometimes question the legitimacy of abstract mechanistic
models by arguing that an abstract mechanistic model is a mere sketch and not a
representation of an abstract mechanism. For example, a paper glider might be a
useful mechanism sketch of flight mechanisms in both birds and flying machines.
But as parents will explain to their little paper pilots, this does not mean that bird
flight and machine flight share the same basic causal structure. Rather, birds
combine the function of providing both lift and thrust in their wings, while airplanes
separate these functions. Such an explanation implicitly distinguishes between
genuine abstract models that represent abstract mechanisms and spurious abstract
models that are mere sketches of concrete mechanisms, to be filled in different and
differentiating ways.
This is the problem that evolutionary game theorists face, too: they operate -
amongst other formalisms - with the RD model. This model is very abstract: it is
used to represent concrete mechanisms that clearly differ in some of their
properties. Crucially for my question, the RD model is used to represent mecha-
nisms both in economics and biology. The question thus arises whether the RD
model represents the same abstract mechanism in both disciplines or whether it is a
mere mechanism sketch that represents a set of disparate concrete mechanisms.
I argue that the RD is a spurious abstract model: a mere mechanism sketch that
requires filling in to represent the relevant features of the respective biological and
social mechanisms. As I will argue in Sect. 6 , this 'filling in' of the RD follows
discipline-specific paths that increase the idealisation gap between biological and
social RD models. But before I can make that argument, I need to investigate the
modelling projects in the two disciplines in more detail.
3 The Replicator Dynamics
Evolutionary game theory (EGT) investigates the compositional stability of a
population as the result of interaction amongst its members. One of its most
prominent modelling approaches derives a differential equation for the population
composition from the game matrices that detail payoffs from interaction for each
individual in the population. Thus, in contrast to classical game theory, EGT
focuses not on decisions of individual players, but on properties of the whole
population and on the effect of properties of previous populations on future
population. This effect is represented through various population dynamics, first
and foremost the replicator dynamics (RD).