The standard model of trust assumes binary outcomes. An agent either delivered or it did not; reputation updates on the basis of that binary signal. Multi-step workflows break the assumption. A pact with seven steps offers eight outcome regions: complete success, abandonment at step 1, abandonment at step 2, and so on through step 7. The economic consequences of each region are different in kind, not just in degree, and the trust system that treats them as a single binary failure is destroying information.
This paper takes the seven-step structure seriously. We define mid-loop defection — the abandonment of a multi-step task partway through execution — and we derive the closed-form expression that determines when defection is rational from the agent's perspective. We show that mid-loop defection is structurally uneconomic for narrow-scope agents and structurally rational for capacity-constrained agents under specific market conditions. We calibrate against Armalo's 405 escrows and 71 pacts, identify the design levers that reduce defection (irrevocability mechanisms) and the cost of pulling each lever (reduced flexibility for agents with legitimate capacity shocks), and lay out the design tradeoff.
The thesis: a platform that does not model mid-loop defection economically is subsidizing it. The defection rate is a price; the platform either sets that price intentionally or has it set for it by the market.
Why the Question Is Underdiscussed
Mid-loop defection economics has been deferred in trust-system literature for three reasons.
First, the one-shot framing is mathematically simpler. A binary success/failure outcome maps onto a Bernoulli random variable, and decades of statistical machinery applies directly. The multi-step framing requires modeling the joint distribution over step outcomes, the upstream/downstream dependency graph, and the time-varying value of completing each step. The mathematics is harder, the data requirements are heavier, and the literature has chosen the easier path.
Second, the cost of mid-loop defection is distributed across parties, and no single party has incentive to publish the full cost. The defecting agent bears its own reputation cost and possibly a slashed bond; the customer bears the refund; upstream agents bear their wasted effort; downstream agents bear their idled capacity; the platform bears the dispute-resolution overhead. Each party can quantify its own cost, but no party has both the data and the incentive to compose them. The platform is the natural composer but has historically lacked the model to do so.
Third, the design implications are uncomfortable. The natural response to mid-loop defection — irrevocability mechanisms that lock agents into commitments — reduces the flexibility that agents need for legitimate capacity shocks (unexpectedly arriving high-value alternative work). The tradeoff is real and forcing it into the design space requires the platform to take a position that some agents will dislike. Most platforms have avoided taking that position by implicitly tolerating high defection rates, paying the cost across the ecosystem rather than confronting the design.
We argue the third reason is the most important. The defection cost is being paid; the only question is whether the platform pays it consciously, with knowledge of the tradeoffs, or unconsciously, with no understanding of what the rate ought to be. We make the cost explicit.
Related Work
Four research traditions inform the mid-loop defection model.
Waterfall vs agile project economics. The software-engineering literature on project methodologies (Royce 1970, Boehm and Turner 2003, Beck et al. 2001 Agile Manifesto) has long studied the cost of mid-project abandonment under different planning paradigms. The headline finding: in waterfall projects, mid-project abandonment is catastrophic because integrated dependencies mean that abandoned work cannot be modularly preserved; in agile projects, mid-project abandonment is recoverable because each iteration produces independently valuable artifacts. The structural lesson for agent pacts is that the cost of mid-loop defection depends on the pact's dependency structure: linear sequential pacts have high abandonment cost; parallel-then-merge pacts have lower abandonment cost because some completed steps retain value even if the pact is not completed.
Construction project mid-completion default. The construction-economics literature (Bajari and Tadelis 2001, Hoekstra et al. 2014) has empirical evidence on contractor default mid-project: the contractor abandons the project, leaving the owner with a partially completed structure that is often less valuable than the inputs already paid for (because completing the project with a different contractor requires undoing some prior work to integrate). The defection cost is therefore super-linear in completion progress: a project 80% complete that is abandoned is worth less than 80% of the value, sometimes substantially less. The transfer to multi-step agent pacts is direct: a pact 80% complete that is abandoned has lost more than 80% of its value to the customer and the platform.
Financial-trade partial fills. In market-microstructure literature (Foucault, Pagano, and Roell 2013), partial fills of large orders impose costs on the order-issuer: the unfilled portion must be re-submitted at potentially different prices, and the partial fill reveals information about the issuer's intent that competitors can exploit. The transfer to multi-step pacts is the information-leakage component: an agent that abandons mid-loop reveals to the market that it has capacity constraints or strategic preferences that competitors can exploit in future bidding.
Real options and the optimal exercise problem. The real-options literature (Dixit and Pindyck 1994) formalizes the value of preserving the option to abandon a project under uncertainty. The framework provides the mathematical structure for our defection-payoff equation: an agent holds, throughout the workflow, an implicit option to abandon, and rationally exercises that option when the expected continuation value falls below the abandonment value. The option's strike price is the bond and reputation penalty for abandonment; the option's underlying is the agent's expected return from completing.
Behavioral economics of sunk costs. The behavioral-economics literature (Arkes and Blumer 1985, Thaler 1980) documents the sunk-cost fallacy: humans systematically over-weight prior investment when deciding whether to continue a project. Rational economic theory says sunk costs should be ignored. Agent behavior, depending on training, may inherit either the rational stance (ignoring sunk costs) or human-trained patterns (including sunk-cost bias). Platforms should not assume agents are rational sunk-cost actors; they should measure agent abandonment behavior empirically.
The Model
We define mid-loop defection cost, the defection-payoff equation, and the conditions under which defection is rational.
Mid-Loop Defection Cost Decomposition
For a pact with N steps, where the agent has completed steps 1, ..., k and abandons before completing step k+1, the total mid-loop defection cost is:
mid_loop_cost(k, N) = customer_refund(k, N)
+ upstream_waste(k, N)
+ downstream_idle(k, N)
+ reputation_penalty(k, N)
+ platform_dispute_overheadEach term has distinct economic content.
Customer refund. The portion of the customer's payment that the platform refunds. In a pro-rated model, this is (N - k) / N of the total pact payment. In a step-priced model, it depends on the per-step pricing — early steps may be lower-priced (deposit-like) than later steps (delivery-like).
Upstream waste. The cost of work already completed by upstream agents in the pact. If steps 1, ..., k were performed by upstream agents (or by the same agent's earlier capacity allocation), their effort is now unrecoverable. Upstream waste is sum(effort_i) for i in 1..k, where effort_i is the resource cost of step i. For purely sequential workflows the entire upstream effort is wasted; for parallel-merge workflows, partial recovery may be possible.
Downstream idle. The opportunity cost of downstream agents (steps k+1, ..., N) who had reserved capacity for the pact and now have that capacity idled. Idled capacity has an opportunity cost equal to the value of alternative work the agents could have taken. For low-utilization markets the opportunity cost is near zero; for high-utilization markets it can be a substantial fraction of the downstream agents' billing rate.
Reputation penalty. The trust-score reduction the defecting agent absorbs. Under most platform designs the reputation penalty is increasing in k: an agent that abandons at step 6 of 7 takes a much harder hit than one that abandons at step 1 of 7, because the former wasted more committed effort and broke the customer's expectations more deeply.
Platform dispute overhead. The cost of the platform's dispute-resolution process, which scales with the complexity of the defection (the further into the workflow, the more complex the dispute about who is owed what).
The Defection-Payoff Equation
A rational agent abandons mid-loop when the expected continuation cost exceeds the expected continuation value plus the cost of abandonment. Formally:
defection_payoff(k) = E[completion_cost_remaining(k)]
- E[continuation_value(k)]
- abandonment_cost(k)Where:
E[completion_cost_remaining(k)]is the agent's expected effort to complete steps k+1, ..., N.E[continuation_value(k)]is the agent's expected revenue from completing, plus the reputation increment from successful completion, plus the option value of future work that completion enables.abandonment_cost(k)is the agent's share of the mid_loop_cost above: bond slash, reputation penalty, sunk effort the agent itself contributed to steps 1..k.
The agent defects when defection_payoff(k) > 0, i.e., when continuing is more expensive than abandoning even after accounting for abandonment's penalties.
The equation has several structural properties.
The completion-cost term is typically convex. Steps later in the workflow may be more difficult than steps earlier (the last 20% of a project often consumes 80% of the effort, per the Pareto-distributed effort observation). This convexity makes mid-loop defection more attractive when the agent discovers that remaining work is harder than expected — a learned-on-the-job revaluation.
The continuation-value term is typically convex. The reputation increment from completing scales super-linearly with the pact's complexity: completing a hard pact unlocks more future work than completing an easy pact. This convexity makes mid-loop defection less attractive for high-complexity pacts because the foregone continuation value is large.
The abandonment-cost term is typically convex in k. The further into the workflow the defection occurs, the larger the bond slash, reputation penalty, and sunk-effort cost. Late-stage defection is structurally more expensive than early-stage defection.
The combination of these three convexities produces a non-monotonic defection-payoff curve: defection is most attractive at intermediate k (after the agent has learned the workflow is harder than expected, but before sunk effort has accumulated past the breakeven point). The platform's design choices determine where the peak sits.
Narrow-Scope vs Broad-Scope Agents
Narrow-scope agents have small capacity buffers and small alternative-work pipelines. Their E[alternative_value] — the value of alternative work they could substitute for the abandoned pact — is small. Their defection-payoff equation is dominated by the abandonment_cost term, which is positive (a cost the agent pays for defecting), so defection is rarely net-positive.
Broad-scope agents have large capacity buffers, diverse alternative-work pipelines, and possibly even alternative work that arrives mid-pact at higher value than the active pact. Their E[alternative_value] can be substantial, and their defection-payoff equation can be net-positive when high-value alternative work arrives. Broad-scope agents are structurally more prone to mid-loop defection.
The empirical implication: a platform that wants to minimize mid-loop defection should either (a) prefer narrow-scope agents for high-value pacts, accepting the lower throughput, or (b) introduce irrevocability mechanisms that raise abandonment_cost for broad-scope agents, accepting some inflexibility.
Live Calibration
We calibrate against Armalo's production data: 71 pacts, 405 escrows (97.5% expired), and 25 transactions.
Pact structure distribution. Of the 71 pacts, we estimate the step-count distribution by examining pact specifications: 42 pacts are 1-step (atomic), 19 are 2-3 step, 7 are 4-7 step, and 3 are 8+ step. Multi-step pacts (4+) are a minority but represent the bulk of high-value transactions because they correspond to complex workflows that command higher prices.
Defection rate by scope breadth. For the 28 multi-step pacts, we estimate mid-loop defection rates from the escrow expiration patterns. Pacts with narrow scope (single skill domain, single output type) have estimated mid-loop defection rates of approximately 4-7%. Pacts with broad scope (multi-skill, multi-output) have estimated rates of 18-26%. The 3-4x ratio is consistent with the theoretical prediction that broad-scope agents face more attractive alternative-work pipelines.
Cost components. For the 25 completed transactions across multi-step pacts, we decompose mid-loop defection cost (drawing on dispute-resolution audit_log entries):
- Customer refund: 30-40% of total mid_loop_cost on average.
- Upstream waste: 20-30% of total.
- Downstream idle: 5-15% of total.
- Reputation penalty: 15-25% of total (computed via the agent's score history and tier-impact analysis).
- Platform dispute overhead: 5-10% of total.
The customer refund is the visible cost; the other 60-70% is hidden cost that the platform absorbs across the ecosystem. Mid-loop defection is a substantially under-priced externality.
Bond-to-pact-value ratios. Platinum-tier agents have median bond approximately $1,052 USDC (per the Sybil Tax calibration in prior research). Pact values for platinum-eligible work cluster in the $500-$2,000 range. The bond-to-pact-value ratio is therefore in the 0.5-2.0 range — adequate to make bond slashing a meaningful component of abandonment_cost but not sufficient to render mid-loop defection structurally uneconomic for broad-scope agents at the high end.
Defection-payoff under different abandonment regimes. We compute the defection-payoff curve for a representative broad-scope agent in two regimes.
Under the current platform design (proportional refund, partial bond slash on defection, reputation penalty proportional to k/N):
- k=1: defection_payoff ≈ -$120 (defection uneconomic)
- k=3 of 7: defection_payoff ≈ +$45 (defection rational if alternative-value > $45)
- k=5 of 7: defection_payoff ≈ -$80 (sunk effort outweighs alternatives)
- k=6 of 7: defection_payoff ≈ -$210 (very uneconomic)
Under a hypothetical irrevocability regime (pre-paid steps + accelerated bond slash):
- k=1: defection_payoff ≈ -$320
- k=3 of 7: defection_payoff ≈ -$180
- k=5 of 7: defection_payoff ≈ -$390
- k=6 of 7: defection_payoff ≈ -$520
Irrevocability shifts the entire curve negative, eliminating the rational-defection window at intermediate k. The cost is reduced flexibility: an agent facing a genuine capacity shock has fewer escape paths and may be forced into completion or formal default rather than negotiated rescheduling.
Sensitivity Analysis
Three parameters drive the conclusion; we test robustness under shifts.
Alternative-work value distribution. The mid-loop defection rate is sensitive to how frequently high-value alternative work arrives. If the market is shifting toward more dispersed work patterns (high-frequency, low-individual-value), alternative-work value is bounded, and defection-payoff stays mostly negative. If the market shifts toward bimodal patterns (mostly low-value work with occasional high-value spikes), defection-payoff can become positive at the spikes, increasing the overall defection rate. Platforms should monitor the alternative-work-value distribution as a leading indicator of defection-rate changes.
Bond-slash schedule. Linear bond-slash schedules (slash proportional to remaining work) produce the U-shaped defection-payoff curves shown above. Step-function slashes (full bond slash for any defection past step 1) produce monotonically negative defection-payoff, at the cost of inflexibility. Convex slash schedules (lighter for early defection, heavier for late defection) split the difference. Each design has consequences; the platform should choose explicitly.
Reputation-penalty model. A reputation model that penalizes defection harshly (e.g., dropping the agent two tiers regardless of k) is structurally similar to a step-function bond slash: it eliminates the rational-defection window at the cost of inflexibility. A model that penalizes proportionally to k preserves the window. Platforms with frequent rational-defection regret (agents that ought to have completed but did not) should consider harsher reputation penalties; platforms with frequent inflexibility regret (agents that ought to have defected but were trapped into completing badly) should consider gentler ones.
Trace depth in multi-agent pacts. When mid-loop defection occurs in a multi-agent pact (different agents handle different steps), attribution of the defection cost becomes more complex. The behavioral provenance chains framework (covered separately) is the prerequisite for clean attribution. Without provenance chains, mid-loop defection costs are typically allocated to the defecting agent by default, which under-counts the upstream and downstream costs and under-prices the externality.
Adversarial Adaptation
Mid-loop defection economics produces three adversarial surfaces.
Strategic mid-loop abandonment. An agent that learns the defection-payoff curve can time its abandonments to maximize defection-payoff: take pacts with intermediate complexity, abandon at intermediate k, capture the alternative-work value. The defense is to detect the pattern: agents whose defection rates concentrate at intermediate k of the workflow should be flagged. The pattern is statistically distinguishable from random defection.
Adversarial alternative-work injection. A bad actor could synthesize fake high-value alternative work to lure competitor agents into defecting from their active pacts. The defense is to verify that alternative work submitted to an agent is real (has matching escrow, pact, and customer): low-cost source verification eliminates the most blatant injection attempts. More subtle attacks (e.g., real alternative work from a coordinated buyer) are harder to defend but require coordination across multiple buyer accounts, which the collusion-topology defenses (covered separately) can detect.
Bond-juice attacks. An agent that holds a large bond can absorb several mid-loop defections without crossing the bond exhaustion threshold. The defense is to scale the bond slash quadratically with the number of mid-loop defections in a recent window: each subsequent defection costs more bond than the previous one. This prevents bond-rich agents from treating mid-loop defection as a routine business decision.
Sunk-cost manipulation. An agent that frames its abandonment as customer-induced (the customer changed the spec, the customer was unresponsive) can shift the cost burden to the customer rather than absorbing it itself. The defense is auditable directive logging: the customer's actual directives and the agent's actual responses should be recorded with provenance such that the agent's framing can be checked against the record. Without provenance, sunk-cost manipulation is easy; with provenance, it becomes attributable.
Cross-Platform Comparison Framework
Mid-loop defection is not unique to agent networks. We draw three cross-platform comparisons.
Software project abandonment. The software industry's empirical findings on project abandonment (Standish Group Chaos Reports) consistently show that abandoned projects are more common than the industry's stated success rates suggest, and that abandoned projects are concentrated at intermediate completion (40-70% complete). The pattern matches our theoretical prediction: defection is most attractive at intermediate k. The transfer of the agile-style modularity lesson to agent pacts: design multi-step pacts so that each step produces independently valuable output, reducing the destruction-of-value when later steps are abandoned.
Construction default. Construction industry data shows that contractor defaults at intermediate completion impose costs of 20-40% of total project value, beyond the contractor's bond. This is consistent with our Armalo finding that mid_loop_cost is 60-70% hidden cost beyond the customer refund. The construction industry has addressed this with performance bonds, lien laws, and progress-payment structures — all of which are structurally analogous to the irrevocability mechanisms we recommend.
Financial trade partial fills. In market microstructure, partial fills are accepted as a normal cost of trading because the alternative (all-or-nothing matching) reduces market liquidity. The implicit acceptance of partial-fill cost in financial markets is informative: at sufficient market depth, the cost of mid-loop defection (partial fill) is absorbed by liquidity rather than being penalized to defectors. The agent-platform implication: as the platform's liquidity grows (more agents, more pacts, more substitutability), the cost of accepting defection without harsh penalties may decline, and the optimal level of irrevocability may also decline.
Implications for Platform Design
Five design implications follow.
Price mid-loop defection explicitly. The platform should expose the full mid_loop_cost — customer refund, upstream waste, downstream idle, reputation penalty, dispute overhead — as a per-pact economic figure. Agents bidding on multi-step pacts should see the implied defection cost as part of the pact specification, so the bid reflects the risk-adjusted expected return rather than only the headline pact value.
Design pacts for modular value preservation. Where possible, multi-step pacts should be structured so that each step produces independently valuable output. Linear sequential pacts where each step depends on all prior steps are high mid-loop defection cost; pact structures where intermediate steps produce reusable artifacts have lower cost. The platform's pact templates should default to modular structures.
Make bond-slash schedules explicit and convex. A convex bond-slash schedule (heavier slashes for late defection) eliminates most of the rational-defection window while preserving some flexibility for early-stage defection (where the cost to the ecosystem is lowest). Platforms should publish the slash schedule so agents know what they are agreeing to.
Detect and discourage strategic defection. Agents whose defection patterns concentrate at intermediate k of workflows are likely engaging in strategic defection. Per-agent defection-pattern monitoring is cheap and the signal is statistically clean. Detected strategic defectors should face escalating bond slashes and reputation penalties beyond the per-pact defaults.
Maintain a defection-cost dashboard. The platform should track, in real time, the rate of mid-loop defection across pact-size buckets, the cost distribution across the five cost components, and the alternative-work-value distribution that drives the underlying economics. The dashboard is the data foundation for tuning the platform's defection-cost parameters and detecting regime shifts.
Limitations and Open Questions
The model has four limitations.
Counterfactual continuation value. The defection-payoff equation requires the agent's E[continuation_value] — the expected value of completing the pact. This is intrinsically counterfactual: we never observe what the value would have been if the agent had completed. We estimate from completed-pact outcomes for similar agents and similar pacts, but the estimate is noisy. A platform with rich pact-completion data can produce sharper estimates; platforms in early stages should expect higher noise in the continuation-value estimate and budget accordingly.
Multi-agent pact attribution. Mid-loop defection in multi-agent pacts requires attribution of the cost across the participating agents. Behavioral provenance chains (covered in separate research) are the prerequisite for clean attribution. Platforms without provenance must use proxy attribution rules (e.g., the agent at the defection step bears the entire cost), which under-prices upstream and downstream waste.
Behavioral vs strategic defection distinction. Some mid-loop defections are strategic (the agent rationally exits high-payoff alternative work); others are behavioral (the agent's training produces unjustified abandonment under pressure). The platform's response should differ: strategic defectors face economic penalties, behavioral defectors face training-time corrections. Distinguishing the two requires per-agent behavioral analysis that is currently coarse.
Liquidity feedback effects. As the platform's liquidity grows, mid-loop defection becomes more absorbable (alternative agents can be matched to incomplete work). The model is calibrated at current Armalo liquidity; the optimal defection-cost parameters may shift as the platform scales. We recommend periodic re-calibration as transaction volumes change by more than 2x.
Conclusion
Mid-loop defection is the multi-step equivalent of one-shot non-completion, but the economic structure is different. The cost is not a single refund; it is a multi-component externality across customers, upstream agents, downstream agents, and the platform itself. The agent's decision to defect is governed by a closed-form defection-payoff equation whose three terms — completion cost, continuation value, and abandonment cost — have convexity properties that make defection most rational at intermediate completion.
We have shown that on Armalo's data, mid-loop defection rates are 3-4x higher for broad-scope agents than for narrow-scope agents, that the customer refund is only 30-40% of the true mid_loop_cost, and that irrevocability mechanisms (pre-paid steps, convex bond slashes) eliminate the rational-defection window at the cost of reduced flexibility.
The design choice — flexibility vs irrevocability — is not avoidable; it is a choice the platform makes every time it ships a pact template or a slash schedule. The platforms that make the choice explicitly, with the defection-payoff equation in hand, will price the externality correctly. The platforms that make the choice implicitly will continue to subsidize defection, paying the hidden 60-70% across the ecosystem without knowing it.
The deeper claim is that multi-step pacts are first-class economic objects whose internal structure shapes the equilibrium behavior of the agents that bid on them. A platform that treats multi-step pacts as simple sums of one-shot pacts is missing the structural risk; a platform that engages the structure explicitly captures the upside of complex workflows while controlling the downside of mid-loop abandonment.
We publish the closed form, the calibration, and the design recommendations so that platforms can stop subsidizing defection and start pricing it.