Leakage Thresholds for Sandwich Equilibria Under Partial Information

We study a partially observed extensive-form trading game around a constant product market maker with one hidden order, public trade direction, and an interval valued signal for the hidden order size. Agents compete in an execution-rights auction to submit robustly admissible sandwich bundles, meaning bundles that remain valid for every hidden order size consistent with the public signal. We give a closed-form admissibility frontier, show that the maximal admissible front-run is simultaneously optimal for pointwise, expected, and worst-case profit, and derive an explicit worst-case profit formula. This yields an exact distribution-free leakage threshold for profitable sandwiching in the presence of fixed execution cost. We then show that, with at least two symmetric traders, every pure-strategy perfect Bayesian equilibrium of the execution-rights auction implements the optimal robust bundle and transfers all positive continuation rent to the auctioneer. Perfect hiding of any positive lower bound eliminates universally profitable robust sandwiching in our model, although post-trade arbitrage may remain. The results isolate an exact threshold phenomenon for strategic trading under partial observability.