Models of Mechanisms: The Case of the Replicator Dynamics - Mechanism and Causality in Biology and Economics - page 91

Fig. 5.5 The belief-learning interpretation of the RD
The only way that learning behaviour generated by stochastic fictitious play differs
from the population dynamics of the two previous models is that they may differ in
speed of passage along similar paths.
The belief-learning model can be graphically presented as shown in Fig. 5.5 .
This interpretation differs in a number of features from BRD. It commences with
agents playing mixed strategies (where all organisms share the same support) rather
than pure strategies. These strategies are not inherited, but adopted and adjusted by
the agents. Furthermore, it makes the crucial extra assumption that the whole
population and all its strategies and payoffs are mentally represented by each
organism. Based on this representation, the agent estimates how other players
will play in the next period. Furthermore, the schema does not interpret payoffs
as fitness, but as subjectively evaluated outcomes. Based on the estimation of
others' future play, and her own subjective evaluations, the agent then chooses
her action as a best reply. It is this deliberation, and not differential reproduction,
that causes differential representation in the population.
6 Relating the Mechanisms
It should be clear from the comparison of the previous section that the three learning
mechanisms are not identical with what the BRD represents. In particular, what kind
of strategies individuals play, how payoffs are realised and what information and
what mental capacities individuals employ in replicating strategies differ consider-
ably between BRD and the learning interpretations of the RD (as well, to a lesser
extent, between these interpretations themselves). Thus, the BRD and the respective
learning interpretations of the RD represent different mechanisms, even though all
these mechanisms are represented by the same RD model.
The RD model thus appears in the first instance as a highly abstract mechanism
sketch. It is used to represent different kinds of mechanisms, but for each of these
representation tasks, it needs to be filled in with a more domain-specific interpreta-
tion or story.
Nevertheless, one might still want to defend the claim that the general RD
represents one mechanism - namely, by arguing that the BRD and the learning
mechanisms all instantiate a more abstract mechanism and that this abstract mech-
anism is represented by the general RD model.
This idea seems prima facie plausible, particularly when one recalls that the BRD
and the learning models themselves are abstract representations of mechanisms. As I
discussed in Sect. 4 , the BRD abstracts from any concrete content of behavioural
plans, from specific species or individuals and from any differences between