Bateson Game III: Robustness Across Learning Schemes A Robustness Audit of Bateson-Trap Pathologies Across Learners

The Bateson Game formalizes strategic ambiguity arising from uncertainty over the inter-pretive frame mapping actions to payoffs, and shows that bounded learning can converge topathological states: a stable “certainty trap” or a persistent “ambiguity trap” [Fathi, 2025]. Anatural and decisive criticism is that the trap taxonomy might be an artifact of a particularlearner. This paper is a robustness audit: we test whether Bateson-trap pathologies persist acrosslearning schemes, including belief-based frame inference, value-based reinforcement learning,Thompson sampling, pessimistic/ambiguity-averse decision rules, and a meta-learner that detectsaction-dependent framing. We introduce a two-channel taxonomy: (i) hard traps based onpreferred-action dynamics (certainty / ambiguity / defensive convergence) and (ii) soft ambiguitycapturing persistent internal uncertainty (entropy/variance/gap-based diagnostics). We isolate“Table-2-like” adversarial cyclical games—where the Sender’s induced frame is Receiver-worst forboth substantive actions—and show that belief-based frame learners are maximally vulnerable:they enter hard ambiguity traps in 100% of games and achieve mean Receiver payoff near −10.Non-belief learners reduce hard ambiguity by ∆ = −0.93 (95% bootstrap CI [−0.94, −0.91]) andimprove payoffs by ∆ = +2.59 (95% CI [2.07, 3.10], game-level bootstrap, n = 150), primarily byconverging to a defensive security action (“Question”).