Batesonized Red Queen Dynamics: Strategic Frame Uncertainty, Costly Recognition, and Endogenous Evasion in Host–Parasite Arms Races

The Red Queen hypothesis posits persistent evolutionary change driven by antagonistic in-teractions. We develop a game-theoretic mechanism for endogenous Red Queen cycling thatdoes not require exogenous environmental stochasticity: a parasite strategically selects a payoff-relevant “frame” (e.g., antigenic presentation) against a host that learns adaptively under frameuncertainty, while meta-communication/recognition (verification) is costly and can be mademore costly by the parasite via an endogenous “opacity” choice. Formally, we apply a Bateson-style information structure—frame uncertainty plus penalized clarification—as an operator ona benchmark two-action reversal game. We prove: (i) an Expected Value of Perfect Informa-tion (EVPI) threshold for when costly recognition is used; (ii) a globally attracting period-2orbit in host beliefs under exploitative “moving goalposts” frame selection (a Red Queen attrac-tor); (iii) a sharp tipping threshold for long-run recognition frequency; and (iv) a closed-formpolicy/opacity selection result under convex evasion costs. We conclude with testable predic-tions mapped to time-shift assays and canonical host–parasite systems (e.g., Daphnia–Pasteuria,Potamopyrgus–Microphallus, bacteria–phage).