Batesonized Competition: Frame Uncertainty in Hotelling–Downs Spatial Games and Stackelberg Quantity Leadership

This paper develops a general “Batesonization” operator that embeds a Bateson Game infor-mation structure—strategic frame uncertainty plus a meta-communication penalty—into canon-ical models of competition. We study two workhorse environments: (i) a Hotelling–Downs spa-tial competition game and (ii) a Stackelberg quantity leadership game with linear demand. Inboth cases, the Bateson architecture erodes classical deterministic predictions: median conver-gence in spatial competition becomes non-robust and can bifurcate into maximal differentiation,while the Stackelberg first-mover advantage collapses to the simultaneous-move Cournot out-come when the follower’s observation/verification channel is Batesonized. All results are provenunder explicit primitives and equilibrium concepts (Perfect Bayesian Equilibrium / SequentialEquilibrium). We additionally provide simulation appendices illustrating (i) ambiguity-trap os-cillation and certainty-trap lock-in in belief-learning dynamics and (ii) transparent Stackelbergconvergence versus Batesonized collapse to Cournot.