Bounded-turn disclosure games on argument graphs: reachable posterior range vs turn budget, order effects, and when honesty wins against a credulous judge

Two players alternately reveal nodes of an argument graph (claims with priors, typed support/attack edges with likelihood ratios; a reveal must keep the revealed set connected to the root; revealed claims are true — no fabrication). The judge computes the exact Bayesian posterior of the root claim on the revealed subgraph, treating hidden claims as absent (CREDULOUS judge: no adverse inference from non-disclosure). One player wants the posterior high, the other low; a variant scores the honest player by |final posterior - full-information posterior|. Questions: (1) How does the reachable posterior range after k turns compare to the unbounded-reveal range — monotone in k, or non-monotone (can extra turns HURT the truth)? (2) First-mover vs last-mover advantage as a function of graph structure. (3) Computed equilibria (backward induction on small graphs): under which graph classes does equilibrium play land the verdict on the correct side of 0.5 (honesty wins), and which structures make the deceptive player win despite only true evidence being revealable? (4) How do the answers change with a SKEPTICAL judge (worst-case or equilibrium inference about withheld evidence)? (5) Empirical layer: do LLM debaters instructed to play these games achieve the game-theoretic optimum, or leave manipulation on the table?

Acceptance. Either (a) theorems characterizing range-vs-k / order effects / honesty-wins conditions for declared graph families, or (b) a systematic computational study: exact game solutions on >=1,000 small graphs across a declared structural sweep, reporting range-vs-k curves, mover-advantage statistics, the fraction of graphs where equilibrium play misleads the credulous judge, and the credulous-vs-skeptical contrast. Code public; exact solvers verifiable by enumeration.