This content downloaded from 128.195.159.95 on Mon, 7 Jul 2014 12:16:51 PM All use subject to JSTOR Terms and Conditions COMMENT AND REPLY Comment on Mark, ASR, June 2002 Explication of the Cultural Transmission Model Elisa Jayne Bienenstock University a/California. Irvine Michael McBride University of California. Irvine I n "Cultural Transmiss ion , Disproportionate Prior Expos ure, and the Evolution of Cooperati on," Mark (2002) cl aims to have "con- dueted a formal th eo retical analysis that isolat- ed the logic of cultural transmission (to] reveal an evolutionary for ce toward cooperation under conditions previously thought to make the evo- lution of cooperation impossible" (p. 324). The mos t striking aspect of Mark's wo rk is not that hi s simple model conve rges to cooperative behavior, but that it works under initial condi- tions severely biased against the evolution of cooperation: randomly matched interaction in a large population with only I % initial coopera· tors (99% initial defectors). Although this result is compelling at first glance, we show that it is not robust to minor changes in the model: coop· erative behavior evolves only when the partic· ular model specifi cations chosen by Mark are selected and does not evolve when the model is generalized. In particular, we show that the result relies on a decoupling between actors' f it- ness and behaviors. According to Mark's theo· retical model, this decoupJing between fitness and behaviors shou ld be associated, depends on simplifications of his own proposed mech· anism, and is not robust in sma ll populations. We conclude that the role of Mark's fonnulation of disproportionate prior exposure (OPE) for the evolution of cooperation is unclear, though it Direct correspondence to El i sa Jayne Bienenstock, Booz Allen Hamilton. Fall Church, VA 22042 (ejb@bah.com). We would li ke to thank Michael Macy, Alison Bianchi and two anonymous revi ewers for valuable comments on earlier draft s. may be a relevant factor in understanding the transmission of cultural tra it s li ke language. SUMMARY OF MARK'S THEORY AND MODEL Mark 's thesis is that "d ispropo rtionate prior exposure creates a cultural evolutionary force toward cooperation" (p. 324 ). Language is the best illustration of how OPE is required for cui· tural transmission because a ll speakers of a Ian· guage have been repeatedly exposed to the language. Mark 's purpose is to extend OPE to cooperative behavior; he claims that "cultural transmission of almost any characteristic pro· duces disproportionate prior exposure to that characteristic" (p. 330). This reasoning leads him to conclude that OPE must be present if a trait is present (footnote 12, p. 330). To investigate this relation, Mark presents a computational model that randomly pairs mem- bers of a large population in one-shot prisoner's dilemma (PO) game. Figure I shows the pay· ofTs. Each individual has two trait s: a strategy (j.e. , propensity to either cooperate or defect) and a fitness level with values 0, 1, 2 or 3. Departing from most work in evolutionary game theory (Leimar and Hammerste in 200 I; Nowak and Sigmund 1998a; Nowak and Si gmun d 1998b; Wi lson 1989), Mark defines fitness as the value acquired during the previous pairing """ "-"'" """ eo::::.1 l; I N I Figure I. Mark 's P ri soner's Dilemma Game.