Refundable Stake Does Not Expand Deterrent Capacity in Long-Lived Delegation: Collateral, Premia, and Pseudonymous Markets
Wulf A. Kaal · 2026
∗Professor of Law, University of St. Thomas School of Law (Minneapolis). Nature and scope of claims. This Article is a theory paper: a reduced-form incentive analysis of refundable collateral in long-lived del- egated relationships among pseudonymous parties. It distinguishes three classes of statement and labels each in place: the author’s results whose algebra survived the adversarial audit protocol described below (the capacity frontier, its cell slopes, and the admission conditions); conditional results whose validity depends on stated open modeling choices (the market layer and any equilibrium-selection role for entry fees); and conjectures (the behavioral decomposition for observed misconduct rates). Complete formal proofs are not contained in this draft. After the author’s initial formulation, the claims below were stress- tested in a nineteen-round adversarial protocol in which three frontier language models (Claude, Grok and Codex), under the author’s direction, alternately attempted to identify counterexamples, algebraic errors, and overstatements. The surviving statements are those that neither system broke, and the audit trail is preserved in the author’s research archive. That protocol is neither peer review nor a substitute for complete formal proofs. Every reference was verified against publisher or authoritative bibliographic records, with resolving links, on August 20, 2026, and each is cited only for the specific statement the verification confirmed it supports. Nothing in this Article predicts the performance of any commercial deployment or constitutes investment, legal, or technical advice. Field environments may diverge from the model in ways the analysis prices only partially, including adversarial populations, filing and adjudica- tion quality, market tightness, real rather than modeled stakes, regulatory and jurisdictional constraints, and the operational, governance, and incentive choices of commercial principals that are not within the auth
Cite: Wulf A. Kaal, Refundable Stake Does Not Expand Deterrent Capacity in Long-Lived Delegation: Collateral, Premia, and Pseudonymous Markets (2026). SSRN: https://ssrn.com/abstract=7322599
PDF sha256: 130ee4e65fb79a9f3a96f6df22408b40c2de76e9ec8fc2bd1c68f0f6a7104333