Good question to ask now, because the model in #2CCJRE is at the point where every term has to earn its keep against the empirical phase. Below are five candidate simplifications, ordered from most conservative to most radical, each with the theoretical grounding and the kind of finding that would warrant adopting it.
Variation A — Collapse the two probabilities
Form: P_win · R − K(s) > OC, with P_win = f(q, θ, s, n)
Theory. Spence/Stiglitz require a separating equilibrium to exist (your Gate 1) and the supplier to be inside the separating set (your Gate 2), but nothing in the theory requires the supplier to consciously decompose the two. Bajari–Tadelis and the auction-theoretic tradition typically work with a single subjective win probability.
What would trigger it.
- Interviews where suppliers do not separate “will quality matter?” from “will my quality be enough?” — they report one judgement, “is this worth pursuing.”
- A factor analysis or coding pattern in which q-, θ- and P_compete-related codes co-load on a single “viability” latent rather than two.
- Quantitatively: tender-design regressors (criteria clarity, price weight, buyer history) and competitive regressors (expected n, incumbency proxies) do not have separable effects on participation — they predict only the joint outcome.
Cost of this move. You lose the analytical leverage that lets you say which of the two failure modes (screening vs. crowding) is binding in a sub-market. Worth keeping the decomposition if even one or two interview cases sharply distinguish them.
Variation B — Collapse R and OC into a relative rent
Form: P_win · ΔR − K(s) > 0, where ΔR = R − OC
Theory. Standard entry models (Bresnahan–Reiss, discrete choice) compare the chosen alternative to the outside option in relative terms. If R and OC are both net-of-own-cost surpluses, only their difference matters. Within a KIBS sub-market with roughly constant sector margin, ΔR is dominated by contract size relative to the supplier’s typical engagement scale.
What would trigger it.
- Interviews where the outside option is consistently described as “doing client work in the same sector at the same margin.” If margins are sector-symmetric, R and OC differ mainly in revenue, not in profitability.
- Difficulty separating R and OC analytically without invoking firm-specific data you do not have.
- This is probably the cleanest theoretical simplification for your thesis: it eliminates the appearance of overlap that bothered you earlier without losing economic content.
Cost. You lose the framing that explicitly says high-OC firms (those with strong commercial pipelines) self-select out — though you can recover it by saying ΔR is small for such firms.
Variation C — Fold OC into K(s) as full opportunity cost
Form: P_win · R − K* > 0, where K* = K(s) + opportunity cost of bid-period resources
Theory. This is the orthodox TCE / Coasean reading: every cost is an opportunity cost. For SMEs in KIBS especially, the relevant outside option is the billable use of the same key personnel during bid preparation — there is no second strategic alternative, just foregone client hours. Williamson would treat the “outside option” as a component of transaction cost, not a separate term.
What would trigger it.
- Interview evidence that “OC” is, in suppliers’ actual reasoning, the opportunity cost of senior staff time during bid preparation rather than a separable strategic alternative.
- Repeated findings that the binding constraint for small KIBS firms is staff-hour scarcity during a 2–4 week bid window — i.e., K(s) and OC are the same resource.
- If you find OC has no empirically traceable referent beyond K(s), parsimony favours absorbing it.
Cost. You lose the connection to the “active commercial pipeline” story for larger firms with multiple lines of business — for them OC is genuinely separate. So this works well for SMEs but flattens an important heterogeneity at the top end.
Variation D — Lexicographic two-stage (drop the multiplication)
Form:
- Stage 1 (categorical): P_screen ≥ θ_min (else no bid)
- Stage 2 (benefit–cost): P_compete · R − K(s) > OC
Theory. Tversky’s elimination-by-aspects (1972), Simon’s bounded rationality, and your own behavioural extension in #9NNAKR. You already say P_screen has a threshold property in #SB6VY2 — this variation simply takes the threshold seriously and stops pretending P_screen is multiplied with anything. Suppliers who fail Gate 1 do not perform a discounted EV calculation; they exit.
What would trigger it.
- Interviews where suppliers describe categorical exits driven by integrity or evaluation-competence concerns, with no probabilistic blending into a cost calculation.
- Quantitative evidence of bimodality in participation as a function of buyer integrity or criteria clarity proxies (rather than smooth gradients).
- This is the variation most consistent with how you have already framed Gate 1 verbally, and with empirical procurement findings on integrity-driven non-participation.
Cost. Slightly less mathematically tidy. But it more honestly represents what suppliers do, and it sharpens the policy claim: improving evaluation quality has categorical effects, not marginal ones.
Variation E — Heuristic ratio (full satisficing)
Form: Bid if K(s) / V < r̄ AND P_screen ≥ θ_min
Theory. Pure bounded rationality — the supplier applies a coarse “burden-to-prize” rule and a categorical integrity filter. No explicit P_compete, no explicit OC. Aligns with how organisations actually triage tender notifications when they receive dozens per week.
What would trigger it.
- Interviews dominated by burden-to-value ratio talk (“not worth it for €15k,” “too much paperwork for the size”), with no calibrated probability reasoning.
- Quantitative analysis where log(V) and documentation-scope proxies explain most variance in participation, and competitive-structure variables add little marginal R².
- Particularly likely for the low-value KIBS segment where formal expected-utility reasoning is implausibly costly to perform.
Cost. You give up the auction-theoretic vocabulary entirely. You also lose the ability to say anything precise about competition effects. Probably too radical for the thesis as a whole, but plausibly the right model for part of the sample (low-value tenders, small firms).
How to use this in the thesis
The pragmatic move is not to pick one ex ante but to commit to the current form as the baseline and pre-register, in your methodology, the empirical conditions under which you would revise to each variation. Something like:
The model as specified is treated as the baseline. Three revisions are entertained ex ante: (i) collapse of P_screen and P_compete into a single P_win if interview coding shows the two are not separately articulated; (ii) substitution of ΔR = R − OC if R and OC cannot be empirically distinguished at the firm level; (iii) lexicographic reformulation of Gate 1 as a categorical filter if interview evidence consistently shows non-probabilistic exit driven by integrity or competence concerns. Each revision is theoretically grounded and would simplify rather than add parameters.
That sentence does three things at once: it shows you are theoretically aware of the alternatives, it makes your model falsifiable in a constructive way, and it preempts the viva question “why this functional form?”
My recommendation
If I had to bet which simplification your data and interviews will actually warrant:
- Variation D (lexicographic Gate 1) is the most likely revision — it matches what you already say verbally in #SB6VY2 and #9NNAKR, and KIBS interview evidence on integrity exits tends to be categorical rather than graded. Adopting it would strengthen, not weaken, the model.
- Variation B (ΔR = R − OC) is the cleanest cosmetic simplification and the one I’d suggest you adopt now even before fieldwork, because it directly resolves the V−C/OC overlap that prompted this conversation.
- Variation A is a fallback if the q/θ/P_compete distinction does not survive coding.
Variations C and E I would keep as theoretical alternatives in a footnote, not as live candidates — C loses the heterogeneity story for larger firms, E gives up too much auction-theoretic vocabulary to be defensible as the thesis model even if it is right for a sub-sample.