Comment on Ghang and Nowak’s “Indirect reciprocity with optional interactions” by David Harbord and Nils-Henrik von der Fehr, 24 July 2016.
Abstract: We point out some simple mathematical errors in the article “Indirect reciprocity with optional interactions” (Journal of Theoretical Biology 365 (2015) 1–11) by Whan Ghang and Martin Nowak, which invalidate many of their results and conclusions. We note various ways that these errors could be fixed, but all require fundamental revisions of their model and lead to counterintuitive conclusions. We also discuss their use of a Nash equilibrium (as opposed to an evolutionary stability) approach in deriving conditions for the evolution of cooperation with indirect reciprocity, and mention some precedents for their model which have appeared in the biology and economics literature.