Abstract
In recent years, many scholars have suggested that the Baldwin effect may play an important role in the evolution of language. However, the Baldwin effect is a multifaceted and controversial process and the assessment of its connection with language is difficult without a formal model. This paper provides a first step in this direction. We examine a game-theoretic model of the interaction between plasticity (represented by Herrnstein reinforcement learning) and evolution in the context of a simple language game. Additionally, we describe three distinct aspects of the Baldwin effect: the Simpson–Baldwin effect, the Baldwin expediting effect and the Baldwin optimizing effect. We find that a simple model of the evolution of language lends theoretical plausibility to the existence of the Simpson–Baldwin and the Baldwin optimizing effects in this arena, but not the Baldwin expediting effect.
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Notes
This investigation is also useful because the learning rule we discuss here falls outside the scope of those considered in Smead and Zollman (2008).
The replicator dynamics is just one of a class of dynamics that captures this idea. The class is known as payoff-monotone dynamics.
These models differ slightly from ours in that they consider so-called “act-based” learning where individuals treat each state or signal as a learning situation distinct from other states or signals. In that way individuals are not learning total contingency plans for every possible state or every possible signal, but only particular moves. Our use of Herrnstein reinforcement presumes that individuals are learning on entire contingency plans.
The discrete time replicator dynamics is more conducive to simulations than the related continuous time dynamics. It should be noted, however, that there are some differences between the two dynamics which may be significant (Weibull 1997).
Here, it is not specified how the trait becomes canalized. This may be important for determining the plausibility of some particular evolutionary path, but is beyond the scope of this paper.
The fact that there are only two possible behaviors in this particular examples can make the interpretation of “novelty” seem artificial. However, similar interpretations and examples could be given for much larger games with many more possible actions.
In this case, a “cost” could actually be beneficial, if deviations somehow resulted in higher payoffs accidentally. The cost is quantified here by looking at the proportion of plays that deviate from the “normal” best-response behavior of the learners and calculating the payoff difference between the normal behavior and the cases where deviation occurs.
We should expect Herrnstein reinforcement learners to take longer to play Defect regularly against cooperators than against defectors, and likewise longer against other reinforcement learners than defectors. Hence, the “error rate” of reinforcement learners is dependent on the strategy being used by the co-player, and thus this example is not subject to the theorems regarding endogenous cost in Smead and Zollman (2008).
This average payoff was determined by running 10,000 independent runs of Herrnstein reinforcement against each pure type and constructing an expanded game using these estimated payoffs.
For instance, in his (1991) he says, “If it weren’t for the plasticity, however, the effect wouldn’t be there” (p. 186). But in his (1995) he weakens this claim, “... their species will evolve faster because of its greater capacity to discover design improvements in the neighborhood” (p. 79, emphasis in original).
Suzuki and Arita (2004) are an exception. They consider strategies in a repeated Prisoner’s Dilemma which include plasticity. Although they do not single it out, they observe a Baldwin optimizing effect in their model as well.
Our informal analysis of novelty presented above does not answer the question here, since we would need to measure directly the convergence speed in different models. This is beyond the ability of the replicator or replicator-mutator dynamics, and would instead require a finite population model. Models such as the Moran process (Moran 1962) might be appropriate for this task. Such a model would conform to our informal discussion of novelty, but space prevents us from discussing it here.
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Acknowledgements
The authors would like to thank Brian Skyrms, Bill Harms, Kyle Stanford, Brad Armendt, and Santiago Amaya for helpful suggestions.
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Zollman, K.J.S., Smead, R. Plasticity and language: an example of the Baldwin effect?. Philos Stud 147, 7–21 (2010). https://doi.org/10.1007/s11098-009-9447-x
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DOI: https://doi.org/10.1007/s11098-009-9447-x