# Investigating incentives around the Deposit Margin

###### tags: `Retrievability Pinning`

:::info
Up to date by August 2022
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## Problem Statement

- The deposit margin ($m_d$) is used as an estimator of an given Provider "effective" collateral.
- The goal of that term is to make sure that the provider will always have enough collateral to pay any incurred slashes.
- By being under-collaterized, there is an increasing risk that the provider will shirk into its commitments.
- Open question: should the protocol handle this kind of event?
- Design goal: minimize risk of shirking.

## Definitions

- $\mathcal{D}_p$: Set of deals associated with provider $p$
- $\mathcal{M}_p = \bigcup p m_{d, D}$: Set of required collaterals associated with provider $p$
- $C^*_p(t) = max(\mathcal{M}_p)$: Required collateral at time $t$ for provider $p$
- $C_p(t)$: Actual collateral at time $t$ for provider $p$
- $s_D = p_d m_{s, D}$: Slash amount associated with deal $D$
- $S_p(t) = \sum_{D \in \mathcal{D}_p} s_D$: Maximum slashable volume at time $t$ for provider $p$
- Metrics
- $\frac{C_p(t)}{C^*_p(t)}$: Collaterization Balance
- Interpretation: values below 1 means that the Provider has less deposits than required.
- $\frac{C_p}{S_p}$: Extrinsic Collaterization Ratio
- Interpretation: related to absolute risk of shirking on a given moment
- $\frac{C^*}{S_p}$: Intrisic Collaterazation Ratio
- Interpretation: related to a priori risk of shirking on a given moment
- Design goals:
- $C_p(t) \gt s$
- Actor goals
- Provider
- Goal 1: Minimize absolute collaterization ($C_p$)
- $\pi_d \propto -C_p(t)$
- Goal 2: Minimize the extrinsic collaterization ratio.
- $\pi_d \propto -\frac{C_p(t)}{S_p(t)}$
- Goal 3: Maximize payment volume
- $\pi_d = \sum_{D \in \mathcal{D}} p_D$
- Goal 4: Minimize slashes
- $\pi_d = -\sum \bar{s}_D$