9 Unmanned Operation: The Limit With the Operator Removed

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v0.28.9 — This text is under construction. The structure of the theory, the propositions, and the empirical conclusions may all change. Overview

Chapter 9
Unmanned Operation: The Limit With the Operator Removed

9.1 The question

Chapter 8 treated a solo business. This chapter asks about its limit: whether a business with no operator at all can stand. Since it is obvious that launching requires people, the question of unmanned operation is confined to steady running, after which the launch cost itself is examined to see how far it can be reduced.

Theoretical quantities in this chapter
$Ω, \hat{Ω}$	Chapter 4	the state space, and the subset envisaged at design time
$λ_{𝑛𝑜𝑣𝑒𝑙}$	this chapter	the arrival rate of $Ω ∖ \hat{Ω}$
$𝒢$	Chapter 4	automation demands a stronger condition than this
$κ_{C} > 0$	Eq. (3.2)	credit issued by the operator as a free period

Table 9.1: Theoretical quantities in this chapter.

9.2 Formalizing “unmanned”

9.2.1 Automation is a stronger condition than measurability

Chapter 4 made $𝒢$ -measurability the condition for a contract to be implementable. Automation is stronger.

Definition 9.1 (Automation). Writing the response down in advance as a measurable function $a : Ω \to 𝒜$ on the state space. $𝒜$ is the set of available responses (a different quantity from fixed assets $A$ , distinguished by typeface).

Proposition 4.1 required $π$ to be $𝒢$ -measurable. Automation adds the requirement that the response be written down in advance. A contract need only be verifiable after the fact; automation does not have that luxury. An algorithm is nothing other than a measurable function specified in advance. Thus

implementable : π is 𝒢 -measurable ⊊ automatable : a specified in advance on \hat{Ω}

(9.1)

The difficulty is that $Ω$ is not closed. Writing $\hat{Ω} \subset Ω$ for the state space envisaged at design time, $a$ is undefined when $ω \in Ω ∖ \hat{Ω}$ arrives. Legal change, a discovered vulnerability, a payment provider’s change of terms, and unforeseen use are such cases.

Proposition 9.2 (Unmanned operation is a function of duration). Writing $λ_{𝑛𝑜𝑣𝑒𝑙}$ for the arrival rate of unforeseen states, the period over which operation can be unmanned is about $1 ∕ λ_{𝑛𝑜𝑣𝑒𝑙}$ . Fully unmanned operation holds for a finite period but not indefinitely.

Remark 9.3 (An upper bound on $λ_{𝑛𝑜𝑣𝑒𝑙}$ can be measured). In the “inside” partition of Chapter 10, responses to unforeseen states leave a record. Modification runs at 0.048 and cessation at 0.030 a year, and arrivals requiring no response cannot be counted, so these are a lower bound on $λ_{𝑛𝑜𝑣𝑒𝑙}$ (Section 18.3, Remark 18.6). The $1 ∕ λ_{𝑛𝑜𝑣𝑒𝑙}$ of this proposition is therefore shorter than 20 years.

The distribution is bimodal. Those that are touched are touched with a median of 42 days; those that are not go untouched for a median of 4.6 years. A mean $1 ∕ λ$ conceals this bimodality.

9.2.2 What is required is not labour but availability

Responding to $Ω ∖ \hat{Ω}$ is not steady labour. Normally nothing is done, and action occurs only on arrival. The structure is the same as family 2-5 (options and warranties) of Part II.

the operator of an unmanned business is short an option on Ω

(9.2)

Delivery $δ$ in normal times can be made zero, but availability cannot. Labour can be reduced without limit; standing by remains. What is called “unmanned” is unmanned in labour as a flow; in availability as an option it is manned.

This is a different kind of constraint from the capacity constraint of Chapter 8. Equation (8.2) bounds the total of delivery; availability bounds the length of an interval over which one cannot respond.

Definition 9.4 (Response deadline and the availability constraint). Write $T_{𝑟𝑒𝑠𝑝}$ for the time allowed between the arrival of $ω \in Ω ∖ \hat{Ω}$ and the response, and call it the response deadline. Writing $u$ for the length of an interval over which the operator cannot respond, the availability constraint is

\sup u \leq T_{𝑟𝑒𝑠𝑝}

(9.3)

Equations (8.2) and (9.3) both have the dimension of time, but they bind different things: the former acts on an integral, the latter on a supremum. Hence no reduction in the amount of labour loosens (9.3). This offers an account of where the practical burden of a solo business lies.

Imposing both together makes the content of that burden more concrete.

Proposition 9.5 (Availability restricts the granularity of capacity). Under (9.3), the time available for delivery is fragmented into intervals of length at most $T_{𝑟𝑒𝑠𝑝}$ . A delivery requiring an uninterrupted stretch longer than $T_{𝑟𝑒𝑠𝑝}$ therefore cannot be performed even when the $Cap$ of (8.2) has room to spare.

Proof. $\sup u \leq T_{𝑟𝑒𝑠𝑝}$ requires that no interval without response exceed $T_{𝑟𝑒𝑠𝑝}$ . An interval devoted to delivery is an interval without response, so its length is also at most $T_{𝑟𝑒𝑠𝑝}$ . A delivery requiring an uninterrupted stretch longer than $T_{𝑟𝑒𝑠𝑝}$ does not fit into such an interval. □

The availability constraint does not reduce capacity; it restricts its granularity. The $T_{𝑑𝑒𝑣}$ of Chapter 8 requires long uninterrupted stretches, whereas operation is a repetition of short responses. Proposition 9.5 derives the difficulty of combining development with operation in a solo business as the intersection of two constraints.

Remark 9.6 (They loosen in different directions). Equation (8.2) loosens by adding people. Equation (9.3) does not loosen without a relief operator, and so long as one is alone the only route is to lengthen $T_{𝑟𝑒𝑠𝑝}$ itself. A longer response deadline is obtained by contractual agreement or by shrinking $Ω ∖ \hat{Ω}$ .

Remark 9.7 (The level of $T_{𝑟𝑒𝑠𝑝}$ differs by component). $T_{𝑟𝑒𝑠𝑝}$ depends on the content of $Ω ∖ \hat{Ω}$ . Chapter 17 decomposes $λ_{𝑛𝑜𝑣𝑒𝑙}$ into four components, and the grace allowed for a published vulnerability differs by orders of magnitude from that for a change in the law. Evaluating (9.3) in practice requires $T_{𝑟𝑒𝑠𝑝}$ by component, which is not measured here.

Remark 9.8 (Correspondence with Knight’s distinction). Variation over $\hat{Ω}$ has a measure defined on it and is therefore risk; both automation and insurance (family 5-4) are possible. $Ω ∖ \hat{Ω}$ is uncertainty, and neither is.

Remark 9.9 (A degree of unmannedness cannot be defined). “How unmanned is it?” cannot be expressed as a ratio.

Measuring on the delivery side does not work. $δ$ carries monetary units through the valuation map $v$ , but $v$ measures value, not effort. The ratio of the value of automated to manual delivery does not express a degree of unmannedness.

Measuring on the response side does not work either. Automation means that $a$ is specified in advance on $\hat{Ω}$ , so a degree would be the ratio of the sizes of $\hat{Ω}$ and $Ω$ . But by Remark 9.8 no measure is defined on $Ω ∖ \hat{Ω}$ .

The obstacle is therefore not the absence of a unit but the absence of a measure, and sharpening the definition does not remove it. Unmanned operation can only be stated as a function of duration, not of degree (Proposition 9.2).

Remark 9.10 (Unmanned operation and profit). If $Φ$ and $C_{prod}$ can be fully specified in advance, they are fully replicable. Competition therefore presses $ϕ_{𝑝𝑟𝑜𝑑} \to 0$ . The closer to fully unmanned, the thinner the source of profit.

One may read profit as the return to the residual that cannot be automated. Network effects and brand create exceptions, so this cannot be asserted flatly, but the mechanism is plausibly at work.

9.2.3 Where a free period fits

A free trial is a state in which $δ$ is supplied with $π = 0$ , that is, the operator extends credit to the customer, $κ > 0$ . It works because the marginal cost is zero, so the cost of extending that credit is near zero. A free trial of a physical good loses inventory; a free period for software costs only infrastructure.

free trial = credit that only a zero-marginal-cost business can issue cheaply

(9.4)

Section 8.5 listed three solutions to the credit bootstrap problem, and this is a fourth: extend the credit oneself in place of having credit. $T_{𝑐𝑟𝑒𝑑𝑖𝑡}$ is being purchased at the cost of $κ > 0$ .

9.3 Decomposing the bootstrap

9.3.1 Each term and where it can be externalized

For each term of (8.11), who can absorb it. The period required for registration with the institutional layer is added as $T_{𝑖𝑛𝑠𝑡}$ .

Term	Content	Externalized to	Price
$T_{𝑑𝑒𝑣}$	building the delivery system	off-the-shelf platforms, payment SDKs, hosting	usage fees
$T_{𝑖𝑛𝑠𝑡}$	registration with the institutional layer	merchant screening by a payment processor, merchant of record	fees
$T_{𝑐𝑟𝑒𝑑𝑖𝑡}$	accumulating credit	a platform’s refund guarantee; or self-funded through a free period	fees, $κ > 0$
$T_{𝑎𝑐𝑞}$	acquiring customers	distribution through stores and marketplaces	sales commission
Enumerating $\hat{Ω}$	designing the envisaged states	not possible	—
Choosing $Φ$	deciding the contract form	not possible	—

Table 9.2: The terms of the bootstrap cost, where each can be externalized, and at what price.

Proposition 9.11 (The irreducible residue). The only two things that cannot be externalized are the choice of $Φ$ and the enumeration of $\hat{Ω}$ .

Externalization has a consistent price: permanently giving up $ϕ_{𝑏𝑎𝑟𝑔}$ . A one-off launch cost is converted into a perpetual cost in the form of fees.

9.3.2 The dominant term by family

Among the types that survived in Chapter 8, the dominant component of the launch cost differs.

Type	$T_{𝑑𝑒𝑣}$	$T_{𝑐𝑟𝑒𝑑𝑖𝑡}$	$T_{𝑎𝑐𝑞}$	Dominant
1-1 one-off digital goods	high	low	low	$T_{𝑑𝑒𝑣}$
2-1 flat access	high	medium	medium	variance
6-4 charging for opportunity	medium	low	high	$T_{𝑎𝑐𝑞}$ (two-sided)
7-4 donation and support	low	high	medium	$T_{𝑐𝑟𝑒𝑑𝑖𝑡}$
5-5 IP licensing	medium	high	medium	$T_{𝑐𝑟𝑒𝑑𝑖𝑡}$

Table 9.3: The dominant component of launch cost for each surviving type.

Noting that the dominant components of 1-1 and 7-4 are complementary suggests a design that splits the launch cost as a transition across families.

Stage	Content
Publishing	accumulate $T_{𝑐𝑟𝑒𝑑𝑖𝑡}$ . No revenue. $T_{𝑑𝑒𝑣}$ advances as a by-product
7-4 support	the first $π$ stands on accumulated credit alone; demands almost no $T_{𝑑𝑒𝑣}$
1-1 one-off sale	the launch is light because $T_{𝑐𝑟𝑒𝑑𝑖𝑡}$ is done. $κ \approx 0$
2-1 flat access	$κ < 0$ , and growth generates cash in the sense of Chapter 5

Table 9.4: Splitting the launch cost through a transition across families.

The leakage term $𝜃$ of Chapter 8 ((8.14)) here works in the opposite direction, as a contribution from publishing to $T_{𝑑𝑒𝑣}$ . The launch cost need not be paid all at once; it can be split by moving across families.

9.4 Limits of this chapter

(1): There is no quantity expressing a degree of unmannedness. As Remark 9.9 states, the obstacle is the absence of a measure, not of a unit, and sharpening the definition does not remove it. This chapter states only what concerns duration.
(2): No level is given for $T_{𝑟𝑒𝑠𝑝}$ . Equation (9.3) can be written, but its right-hand side differs by component of $Ω ∖ \hat{Ω}$ and no value is identified (Remark 9.7).
(3): The inverse relation between unmannedness and profit is only a mechanism noted. No verification, including the treatment of counterexamples such as network effects and brand, has been carried out.
(4): No price is given for externalizing the launch cost. Table 9.2 lists where each term can be externalized but gives no numbers. Chapter 17 measures them.

Chapter 9 Unmanned Operation: The Limit With the Operator Removed