Refundable Stake does not Expand Deterrent Capacity in Long-lived Delegation: Collateral, Premia, and Pseudonymous Markets

Abstract

Practitioners of delegated pseudonymous markets, from proof-of-stake validation to agent economies, commonly assume that a slashable, refundable bond deters misconduct: the operator who cheats loses the stake, so a larger stake buys more honesty. This draft reports the central result of a formal project testing that assumption: in the strict long-match limit, increasing refundable escrow does not expand the credible capacity frontier. In a model where identities can be discarded and re-minted at negligible cost, a refundable bond released at exit pads the operator's walk-away value by the full release-discounted principal; custody carry is an additional tax. In the strict long-match limit, refundable escrowed principal weakly contracts the credible capacity frontier in all four cells of a two-by-two regime map spanning exit versus in-place misconduct and leaky versus captive stake: the contraction is strict in both exit cells and strict in both stay cells if and only if the adjudication probability is positive. The relationship premium supplies the continuation-value component of deterrence. The capacity frontier is identically $\theta X \le P + \varphi (d_h - R) F$ against exit misconduct and, at the baseline with no clawback and no continuation damage, $\theta X \le p P + p [d_h - (1-s) \delta_E] F$ against in-place misconduct. Those displays are accounting identities at a given $(P, F)$; the envelope derivatives in $F$ are the slopes reported below, which already include the decline of $P$ in $F$. Away from the limit, escrow has a positive marginal effect only under turnover-funded admission conditions derived in closed form; at the ideal leaky-exit corner this requires timely filing coverage above a floor that exceeds one in the strict long-match limit with positive carry. The result yields a regime-general capacity prediction; deriving predictions for observed misconduct rates requires an additional behavioral model, offered here as a conjecture. A second, conditional result endogenizes the market outside option and bounds admissible entry fees; whether a small fee also selects among formation equilibria remains open pending an extensive-form formation game.