# kaal:claim:7322599-004

**Claim.** For long-lived delegation with positive carry, the marginal capacity effect of refundable principal is strictly negative in both exit cells and, whenever adjudication probability is positive, in both stay cells; the relationship premium is the scalable continuation-value component of deterrence.

**Type.** mechanism  **Support.** argued

**Holds when.**

- the strict long-match limit with positive custody carry

**Source quote.**

> For long-lived delegation with positive carry, the marginal capacity effect is strictly negative in both exit cells and, whenever the adjudication probability is positive, in both stay cells: refundability raises walk-away value and imposes carry, so additional principal fails to expand long-match capacity, and the relationship premium, the value of staying over leaving, is the scalable continuation-value component of deterrence.

**From.** Wulf A. Kaal, *Refundable Stake Does Not Expand Deterrent Capacity in Long-Lived Delegation: Collateral, Premia, and Pseudonymous Markets* (2026), 1 Introduction, page 3

**Cite as.** 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

**Verify.** sha256 of source PDF `130ee4e65fb79a9f3a96f6df22408b40c2de76e9ec8fc2bd1c68f0f6a7104333` at https://raw.githubusercontent.com/wulfkaal/Academic-Papers/main/papers/pdf/Kaal%20-%202026%20-%20Refundable%20Stake%20Does%20Not%20Expand%20Deterrent%20Capacity%20in%20Long-Lived%20Delegation%20Collateral%2C%20Premia%2C%20and%20Pseudonymous%20Markets.pdf

**Topics.** risk-and-incentives, economics, consensus-and-security, reputation

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