The Economics of Inward Migration: Relocation versus Densification for Computation-Maximizing Civilizations

1. Introduction

1.1 The pricing gap

Three papers precede this one. The Macro Transcension Hypothesis (Swanson 2026a, hereafter Paper A) argues that rapidly spinning massive black holes in dense old stellar systems are the global optimum among present-day environments for long-term computation, and identifies Omega Centauri as the most accessible test system. A critical review of the inward-migration family (Swanson 2026b, hereafter Paper B) places that hypothesis among six decades of related proposals and grades their falsifiability. An observational companion (Swanson 2026c, hereafter Paper C) specifies the instrument-matched campaign. Paper B also catalogued the family's open problems, and its third problem motivates this paper directly: the economics of the migration itself has never been worked out.

The gap is specific. Bostrom (2003) priced delay: every century of postponed expansion forgoes an irrecoverable harvest of free energy. Bennett et al. (2019) priced dormancy: free energy not collected promptly is lost, so the aestivation strategy of Sandberg et al. (2016) forfeits most of what it hoped to save. Nobody has priced relocation. A lineage that migrates abandons its accumulated local infrastructure, spends 10⁴–10⁶ years in transit, accepts a risk of total loss en route, and only then begins to collect a payoff that is, by the physics of Paper A, orders of magnitude larger per unit of everything. Whether that trade clears depends on quantities the inward-family literature has so far left unmodelled: discount rates, hazard rates, transit risk, and the option of sending a seed instead of moving.

This matters beyond bookkeeping. If migration clears the trade only for implausibly patient agents, the inward family loses its force as a Fermi solution regardless of the destination physics. If it clears easily, the family's incomplete-compliance problem (Paper B, problem P4) sharpens into a quantitative question: what fraction of lineages must migrate for the observed silence to follow? Either outcome constrains the family.

1.2 Claims and non-claims

The paper makes three claims:

1. (Decision analysis.) Under the stated utility and payoff kernels, the choice among stay, migrate, and seed-and-stay reduces to closed-form threshold conditions on the discount rate, hazard rate, transit time, and destination multiplier (Section 4).
2. (Hybrid dominance in a band.) The seed-and-stay hybrid dominates both pure strategies in a band extending modestly beyond the migration threshold (to roughly 1.7× the threshold at physical seed costs), because the seed's cost is negligible against local output while the exponential deferred-payoff discount closes the window quickly for impatient lineages (Section 5).
3. (Population corollary.) Folding the decision rule into a mixed population yields the expected thinning of the loud population and a new residue, the Matrioshka-to-quiet-cluster sky ratio, that archival infrared surveys already constrain (Sections 6–7).

We do not claim the parameter priors are measurable; the value of the analysis is the structure of the crossover, not point estimates. We flag model dependence throughout (Section 8).

2. The decision problem

2.1 Agent, utility, and strategies

Consider a technological lineage established at a planetary system a distance d from the nearest system satisfying the Paper A selection criteria (an IMBH of 10³–10⁵ M_☉ in a dense, old, quiescent cluster). Following the family's shared premise, the lineage values integrated computation. Its utility over a policy π is

where C_π(t) is the computation rate delivered at time t (bit-erasures per second, the binding currency by the Landauer accounting of Paper A, Section 4.2) and ρ ≥ 0 an exponential discount rate. We use exponential discounting for tractability and revisit hyperbolic alternatives (Laibson 1997) in Section 8; the patient limit ρ → 0 recovers the Ramsey (1928) zero-discount benchmark, which several authors argue is the only defensible rate for agents with unbounded horizons (Bostrom 2003).

Three strategies span the space:

Strategy H is not exotic: it is the architecture Paper A already assumes (gram-to-kilogram scouts, then seed factories), read as an economic option rather than a mission profile. What has not been stated before is its dominance structure (Section 5).

2.2 Parameters

Table 1 collects the parameters and fiducial values. Transit time uses Paper A's beamed-sail speeds (0.1–0.2c) and the distance to ω Cen (5.49 kpc; Häberle et al. 2025) as the fiducial destination, giving τ_transit ≈ 0.9–1.8×10⁵ yr; we fold construction (≲10³ yr to first ISCO-swarm operation; Paper A, Section 6) into a single τ = 10⁵ yr fiducial. The bare cruise time at the tabulated v = 0.15c is d/v = 1.19×10⁵ yr, so the round fiducial corresponds to an effective ≈0.18c; Table 1 states the bare number so the rows can be checked independently. Beamed-sail launch provides no deceleration at an unprepared destination, and braking by magsail (Zubrin & Andrews 1991; Perakis & Hein 2016) or by photon-assisted maneuvers (Heller & Hippke 2017) can multiply the cruise time by a factor of a few; because the threshold of Section 4 scales linearly in 1/τ, we propagate this allowance explicitly there (Table 1a) rather than absorbing it into the range. The hazard rate λ prices the goal-stability problem (Paper B, problem P2): the probability per year that the lineage ceases to pursue the plan, through value drift, fragmentation, or extinction. We do not claim to know λ; it enters the thresholds additively with ρ, which is the analytically convenient way to carry an unknown.

3. Payoff kernels

3.1 Strategy S: the Matrioshka ceiling

A complete Dyson-type collector intercepts the stellar output, L_* = 3.8×10²⁶ W for a solar analogue (Dyson 1960). Computation against the ambient sink is bounded by the Landauer cost at the effective radiator temperature (Landauer 1961; Bradbury 1999): the innermost shells run hot and fast, the outermost approach the CMB floor T_γ = 2.7 K, and the whole stack is radiator-limited, the constraint Bradbury (1999) identified as binding. An upper bound that ignores every engineering loss is

available after a build time we absorb into the timeline as effectively immediate on the scales of interest (10²–10³ yr; Armstrong & Sandberg 2013). Strategy S also faces a slow ceiling decay (stellar evolution) that we neglect: neglecting it favours S, which is the conservative direction for our conclusion.

Equation (2) is not attainable even in principle, and it matters why not. Rejecting the full L_* at T_rad → T_γ requires zero net flux through infinite radiator area; the standard trade is that radiated power scales as T_rad⁴ while the erasure cost scales linearly in T_rad, so finite architectures optimize at T_rad a few times T_γ and forfeit one to two orders of magnitude in C_S (Sandberg et al. 2016; Bennett et al. 2019; Badescu & Cathcart 2000). We nonetheless carry the unattainable bound, because any downward correction to C_S raises the destination multiplier G and moves every threshold below in migration's favour: Eq. (2) is the conservative choice for the stay option.

3.2 Strategy M: the IMBH platform

At the destination, the sustainable power is bounded above by the Eddington luminosity of the host, L_Edd ≃ 2.5×10³⁵ W at 2×10⁴ M_☉ (Paper A, Eq. 2), a factor ~10⁹ (6.6×10⁸, rounded) over the solar Dyson ceiling. Eddington is capacity, not fuel: the ambient intracluster medium feeds only ~10⁻⁴ of the Eddington rate by Bondi accretion, a power ratio of ~10⁶ (Paper E, Section 2.7); reaching the 10⁹ figure requires imported or harvested mass, at the cost of visibility. The erasure cost against a horizon sink falls by a further factor ~10¹² (Paper A, Section 4.2). The full multiplier on Eq. (2) is therefore formally 10¹⁸–10²¹; we adopt

as the fiducial, crediting the migration payoff with the power ratio only. Two reasons for this deliberate understatement. First, horizon-sink disposal shifts the binding constraint to waste-heat transport (Paper A, Section 4.2), whose engineering efficiency is unmodelled; using the power ratio alone keeps the kernel on demonstrated physics. Second, every conclusion below strengthens monotonically in G, so a conservative G makes the thresholds conservative. Readers preferring the full stack may substitute G = 10¹²–10²¹, or the ambient-fed G = 10⁶; the thresholds move by the logarithm only (ρ* ≈ 1.3×10⁻⁴ yr⁻¹ at G = 10⁶ versus 2.0×10⁻⁴ at 10⁹: three decades of multiplier for a factor 1.5 in threshold; Section 4). One accounting caveat: if computation at either site is performed reversibly (Bennett 1973), erasures are not proportional to useful computation and the two sites' conversion factors could in principle differ. Because G is a ratio of erasure budgets, architecture-dependent reversibility factors cancel to first order when both sites use the same logic family, which is the natural assumption for a single lineage.

3.3 Discounted values

With C_S available from t = 0 and C_M from t = τ with probability p_s, and with the hazard rate entering as an additional exponential attrition on plan continuation, the strategy values under Eq. (1) are

Equation (6) treats the two payoff streams as additive, which is exact if the lineage's utility is linear in computation and the seed's draw on local resources is the fraction f; Section 8 discusses when additivity fails (identity-centred utilities that do not value a forked descendant's computation).

Figure 1 shows the undiscounted rate histories: S delivers early and low, M late and high, H both.

4. Crossover conditions

4.1 Migrate versus stay

From Eqs. (4)–(5), U_M > U_S reduces to

The threshold depends on the enormous multiplier only through its logarithm: the structural reason the result is robust to the order-of-magnitude uncertainties in G. At the fiducials (G = 10⁹, p_s = 0.5, τ = 10⁵ yr),

corresponding to a combined discount-plus-hazard half-life t_1/2 = ln 2 / ρ* ≈ 3,500 yr (the "planning" reading holds at λ = 0). Any lineage whose effective concern horizon exceeds a few millennia (a modest demand against the 10⁸-yr coherence the family's architectures assume elsewhere) prefers migration to densification. Under the full efficiency stack (G = 10²¹) the threshold rises to ρ* ≈ 4.8×10⁻⁴ yr⁻¹ (t_1/2 ≈ 1,400 yr); under a pessimistic p_s = 0.01 it falls only to 1.6×10⁻⁴ yr⁻¹. Transit risk is nearly irrelevant inside the logarithm; the lever that matters is τ.

Because ρ* ∝ 1/τ linearly, τ is the one parameter where a factor of a few moves the answer, and the deceleration allowance of Section 2.2 acts on τ directly. Table 1a propagates it: if braking multiplies the cruise time by 2–3, the threshold falls to 0.7–1.0×10⁻⁴ yr⁻¹ and the headline half-life lengthens to ~7–10 kyr. The qualitative conclusion (patience horizons of millennia, against the 10⁸-yr coherence assumed elsewhere in the family) is unchanged; the quoted 3,500-yr figure is the no-braking end of the band.

Figure 2 maps ρ* against destination distance for the beamed-sail speed range, marking named Galactic targets. Because τ ∝ d, the threshold scales as 1/d: closer acceptable destinations relax the patience requirement proportionally, which is one economic reading of Paper A's selection pressure toward the nearest adequate system rather than the best one.

4.2 What the threshold means

Equation (7) converts the inward-family debate into a single empirical-psychological question: do long-lived technological lineages discount the far future at more or less than a few parts in 10⁴ per year? The literature's positions map onto the two sides. Bostrom (2003) argues that agents with astronomical stakes should approach ρ = 0; on his side of the line, migration dominates by many orders of magnitude. Steep discounters (lineages whose institutions cannot sustain plans beyond centuries) stay home and densify, and for them the inward family predicts nothing. The threshold also prices the goal-stability problem: since λ enters additively, Eq. (7) says the plan need only survive attrition at the same few-per-10⁴ annual rate during the transit window, not for the 10⁸-yr exploitation phases that follow; post-arrival value drift changes who enjoys the payoff, not whether the dynamical residues of Paper A get laid down.

5. The hybrid result

5.1 Dominance

Comparing Eq. (6) with Eqs. (4) and (5): U_H > U_M always (the stay component is pure addition), and U_H > U_S whenever

The right-hand side at fiducials is ~5×10⁸ e^{−20(ρ+λ)/ρ*}, and the exponential is merciless: the tolerable seed cost is ~1 at the migration threshold, ~2×10⁻⁹ at twice the threshold, and ~10⁻⁷⁸ at ten times it. For the physical seed cost, gram-to-kilogram payloads plus a launch array giving f ≲ 10⁻⁶ against a Dyson-scale economy (Lubin 2016; Freitas 1982), the breakeven sits at (ρ + λ)τ = ln(G p_s/f) ≈ 34, i.e. ρ + λ ≈ 1.7ρ*. The hybrid therefore dominates both pure strategies in a band extending roughly 70 per cent beyond the migration threshold, cheap for the patient and worthless for the impatient; outside the band the choice reverts to the pure S-versus-M crossover of Section 4, and the hybrid also fails when the utility is non-additive across descendants (Section 8).

5.2 Consequences

The dominance of H restructures the Fermi implications of the family in three ways.

First, compliance is cheap for the patient. The incomplete-compliance objection (Paper B, problem P4) imagines lineages weighing a costly relocation and many declining. Under H, within the dominance band, there is no relocation to decline: dispatching seeds is compatible with staying and the marginal cost is a rounding error. The question "what fraction migrates?" becomes "what fraction of computation-valuing lineages sits below roughly 1.7× the patience threshold?" — compliance is displaced from economics onto the distribution of ρ + λ, which the family cannot measure but no longer needs to argue about qualitatively.

Second, destinations saturate early. If seeds are cheap, the nearest adequate IMBH systems receive seeds from every computation-valuing lineage in their neighbourhood, and first arrival plausibly matters. This turns the uncontested-claim criterion of Paper A (criterion 3) into a race dynamic of the kind Hanson (1998) analysed for interstellar colonization generally, in which selection favours the fastest and least encumbered colonizers of contested oases, and it implies that the residues of Paper A's P4 should be present in suitable systems even if no lineage ever "migrates" in the whole-population sense. One scope note: the threshold of Eq. (7) is a single-agent calculation, and competition for contested oases only lowers it, since preemption adds option value to early arrival; Eq. (7) is therefore an upper bound on the patience required.

Third, the loud residue does not vanish. Under pure M, migrated lineages leave planetary space entirely and the sky is silent. Under dominant H, the stay component continues local densification, whose Matrioshka waste heat is the classic detectable technosignature (Dyson 1960; Wright et al. 2014). The hybrid therefore predicts both residue classes in linked proportion, the basis of the new population statistic in Section 7.

6. Population consequences

6.1 A mixed-population frame

Let a fraction x of long-lived technological lineages be expansionists, supplying the loud signals whose absence constitutes the paradox (Hanson et al. 2021; Olson 2015), and among expansionists let q be the probability of being susceptible to the inward gradient (holding the family's P1 optimization goal alongside expansionist behaviour). Within the susceptible subset, let m be the fraction whose parameters fall below the (hybrid-enlarged) threshold of Section 5: the fraction that acts on the gradient at all. The parameters are nested conditionals, so the product w q m below is a proper capture probability.

The inward family's contribution to the silence is the claim, argued qualitatively in Paper A, that the maximizer subset contains the oldest and most capable lineages, so its withdrawal from loud behaviour thins the expected loud population disproportionately. The expected number of loud civilizations in a survey volume containing N lineages is

where w ∈ [0, 1] is the overlap weight: the fraction of would-be expansionists whose lineages are captured by the maximizer gradient before or during their expansion phase. Equation (9) identifies only the product w q m: a measured N_loud constrains one number, and the (q, w) grid below is a re-parameterization of that single degree of freedom, useful for exhibiting which value combinations reach it, not evidence of two independently constrained parameters. For the potential-expansionist count N x, the dissolution analysis of Sandberg, Drexler & Ord (2018) shows that reasonable uncertainty over the Drake factors puts substantial probability on N x of order unity as well as on large values. Table 2 evaluates the silence-compatibility condition N_loud < 1 across the (q, w) grid for a fiducial N x product. The table's message matches what Papers A and B anticipated: inward migration alone dissolves the paradox only at high capture (w q m → 1); at moderate capture it thins the expectation by factors of a few and the balance must come from conventional rarity. The new content is the row structure: hybrid dominance enlarges the acting fraction m to everything below roughly 1.7× the patience threshold (Section 5), so m stays a live parameter set by the ρ + λ distribution, and the residual uncertainty splits between patience (m) and values (q, w).

6.2 Relation to grabby-aliens selection

The Hanson et al. (2021) machinery conditions on our early arrival to bound the density of loud expanders. Equation (9) plugs into that frame by modifying the loud fraction while leaving the arrival-time statistics unchanged: inward capture reduces the volume-conversion rate of loud lineages without changing when civilizations arise. A full integration (re-deriving the grabby-aliens posterior with a capture term) is beyond this paper's scope and is the natural next step for whoever takes up Paper B's problem P1; Eq. (9) supplies the term to insert.

7. Observational corollaries: the residue ratio

Hybrid dominance predicts linked residues: for every lineage acting on the gradient, a continuing local densification (Matrioshka-class mid-infrared source) and a seeded quiet-cluster system (the Paper A dynamical residues: anomalous spin, suppressed accretion, core depletion). Pure M predicts quiet clusters without Matrioshka sources; pure S the reverse. The observable is the sky ratio

which is 0 under pure M, of order (n_lineage/n_target) under hybrid H, and unbounded under pure S — where n_lineage/n_target is the ratio of acting lineages to adequate destination systems in the relevant volume (several lineages can seed one cluster; one lineage densifies one home system). The Milky Way contains ~150 globular clusters of which a handful satisfy the Paper A criteria, so under H with even a few Galactic lineages the formation-rate ratio is R_sky ≳ 1. The observed ratio carries a lifetime factor on top: abandoned Matrioshka-class swarms grind to debris by collisional cascade within 10²–10³ yr (Paper E, Section 3.3), while the quiet-cluster dynamical residues persist for gigayears, so R_sky,obs = R_sky × (t_Matrioshka/t_residue) and the infrared branch of the prediction is conditional on maintained, long-lived home installations.

This puts existing null results to new work. Galactic bounds on N_Matrioshka come from Carrigan's (2009) IRAS Dyson-sphere search, the Gaia/2MASS-selected candidate searches (Zackrisson et al. 2018), and the Project Hephaistos series: Suazo et al. (2024) report seven unresolved Galactic candidates surviving their photometric cuts, most or all of which subsequent analyses attribute to hot-dust-obscured background AGN contamination (Ren et al. 2024; Blain 2024; Ren et al. 2025). Together these bound N_Matrioshka in the Galaxy at or near zero over their completeness ranges, pending contamination analysis of the surviving Hephaistos candidates; the Ĝ surveys (Wright et al. 2014; Griffith et al. 2015) bound waste heat for external galaxies and constrain the population statistically. Through Eq. (10), those bounds propagate to the hybrid branch conditionally on maintenance: if R_sky,obs ≳ 1 and N_Matrioshka ≈ 0, then N_{quiet-cluster residue} ≈ 0 too, and the family's Galactic prediction concentrates on the pure-M and short-maintenance corners: lineages whose utilities are non-additive across descendants (Section 8) or whose home infrastructure is dismantled at departure. The Paper C campaign tests that corner directly at ω Cen. Conversely, a confirmed Paper A residue (a near-extremal spin on a gas-starved IMBH) with a continuing Matrioshka null would be evidence about the utility structure of whatever laid the residue down: it would indicate migration without a maintained home presence, the signature of either whole-lineage relocation or post-departure home abandonment. That a spin measurement could carry information about value structure is an inference this pricing framework licenses; we state it in advance of any data.

The archival anomaly-detection agenda of the Dyson Minds workshop (Curtis et al. 2026) and the cluster-ranking metrics of Huang, Tao & Zhang (2026) both operate on the two source classes Eq. (10) links; a joint analysis (ranking clusters and IR-anomaly candidates in the same volume and testing the correlation Eq. (10) implies) is executable from public archives and is, to our knowledge, unproposed.

8. Limits and objections

8.1 Model dependence of the utility

Equation (1) assumes utility linear in computation rate and additive across locations and descendants. Identity-centred utilities break additivity: a lineage that values only its own continuous thread of computation may not credit a forked seed's output, restoring the pure S-versus-M choice of Section 4, which is why the crossover analysis is retained rather than replaced by the hybrid result. Satisficing utilities (compute enough, not most) exit the framework entirely; they belong to the sustainability solution (Haqq-Misra & Baum 2009), not to the inward family.

8.2 Discounting form

Exponential discounting is the tractable choice; hyperbolic discounting (Laibson 1997) cuts both ways. Hyperbolic agents are time-inconsistent: the deciding present self applies its steep short-run rate to the whole deferred payoff, so hyperbolic curvature confers no automatic pro-migration advantage, and naive hyperbolic agents perpetually postpone. Sophisticated ones may commit early, for which the seed is a natural commitment device. A genuinely zero-discount agent (Ramsey 1928; Bostrom 2003) needs no analysis: migration dominates unboundedly.

Uncertainty about the discount rate pushes the same direction, and more forcefully. Under gamma (declining) discounting (Weitzman 1998, 2001), an agent uncertain over its own ρ values the far future by the expectation of the discount factor, giving a certainty-equivalent rate

which declines with horizon toward the minimum plausible rate: the patient scenarios dominate the expectation at long t. An agent uncertain whether its ρ is 10⁻³ or 10⁻⁶ has ρ_eff ≈ 10⁻⁶ at t = τ = 10⁵ yr, far below the threshold of Eq. (7). Migration therefore requires only uncertainty about patience, not patience itself, which strengthens the case beyond the exponential baseline. For calibration in the other direction, empirical institutional discount rates are 10⁻²–10⁻³ yr⁻¹, failing the threshold by one to two orders of magnitude: the framework describes old lineages, not present-day institutions.

Why not wait for faster sails? Heller (2017) showed that a civilization expecting propulsion to improve faces an incentive trap: launching now can be dominated by waiting for a faster vehicle that overtakes the earlier one. In this framework the trap does not bind. Waiting costs discounted utility at the rate ρ + λ on the entire deferred payoff, while speed improvements enter only through τ ∝ 1/v inside the same energy economics that already caps beamed sails at 0.1–0.2c; a bounded reduction in τ cannot repay an open-ended delay, and the seed option makes the launch cost too small for the saving to matter.

8.3 The hazard rate is not a solution to goal stability

Folding P2 into λ prices the problem; it does not solve it. What the pricing shows depends on what λ means. If λ is lineage death, it cancels from both strategies after transit and coherence is required at the few-per-10⁴-per-year level during transit only (Section 4). If λ is plan abandonment or value drift, a drifted stay-home lineage still computes while a drifted mid-transit lineage delivers nothing, so λ binds over the whole horizon and the transit-only reading fails; the results above carry the lineage-death reading, and the drift reading favours seeds, whose automation (a payload that does not deliberate en route) meets the transit demand by construction. The deep version of P2 (whether the destination civilization retains the values that sent it) remains open and remains, as Paper B noted, not an astronomy problem.

8.4 Parameter unmeasurability

q, w, ρ, λ are distributions over agents we have never observed. The defensible claims are structural: the logarithmic insensitivity of the threshold (Eq. 7), the dominance region of the hybrid (Eq. 8), and the sign of the residue-ratio prediction (Eq. 10). Point estimates in this paper are fiducials for orientation, not forecasts.

8.5 Outward counter-positions

Ivliev (2026; preprint, submitted to Acta Astronautica) argues from a comparable automation premise to the opposite directional conclusion: once autonomous AI industry crosses a capability threshold, quiet outward expansion through low-mass probes and seed factories becomes too cheap for any civilization to refuse, and the silence reflects expansion signatures too weak to detect rather than migration. The two frameworks agree that seeds are nearly free (his threshold argument and our Eq. 8 are the same observation) and disagree about the objective: under our kernels the same cheap automation buys more computation per unit resource by seeding inward than by saturating stellar systems, so the disagreement reduces to whether coverage or computation is the maximand, i.e. to the distribution of terminal values already carried by q in Section 6.

8.6 Anthropic caveats

As with Paper A, our own existence as a young loud lineage neither confirms nor embarrasses the analysis; the framework describes the asymptotic behaviour of old lineages, and we are not one. Self-indication corrections to the population frame of Section 6 are absorbed into the grabby-aliens integration deferred there.

9. Conclusion

Paper B posed the question this paper answers: under what conditions does relocation to a thermodynamically privileged destination beat staying home and building? The answer has three parts. The crossover between migration and densification is a patience threshold, ρ + λ < ln(G p_s)/τ, whose logarithmic form makes it robust to the large uncertainties in the destination multiplier and transit risk; at fiducial parameters it asks only for planning half-lives beyond a few thousand years. The seed-and-stay hybrid dominates both pure strategies in a band extending roughly 70 per cent beyond that threshold, which displaces the incomplete-compliance problem from economics onto the joint distribution of patience and the optimization goal. And the hybrid's linked residues yield a population-level prediction, Matrioshka formation at least as frequent as cluster engineering, that existing infrared nulls constrain conditionally on maintenance lifetimes, concentrating the family's surviving parameter space on the pure-migration and short-maintenance corners that the ω Cen campaign of Paper C tests directly.

The broader point is methodological. The inward family has argued from thermodynamic gradients (Paper A), been organized and graded as a literature (Paper B), and acquired a costed observational program (Paper C). What it lacked was a demonstration that the gradient is economically actionable by agents with finite patience and fallible institutions, the step where favourable gradients often fail. That demonstration is now on the table, in closed form, with its assumptions priced and its observational consequences stated in advance. Whether any agent has ever faced the decision is a question for the instruments.

References