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Chapter 8 Practice and a Pre-registered Trial

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Chapter 8 Practice and a Pre-registered Trial

Note

The checklist in this chapter is a thinking tool for preparing a negotiation, not legal advice. The validity of contract terms, liquidated damages and penalties depends on the governing law; consult a lawyer qualified in the relevant jurisdiction before signing. The aim of the checklist is to help you see your own position and the other side’s clearly, not to help you deceive them: Chapter 5 showed that only genuine, verifiable commitments can work reliably.

Part 1 A four-step mechanism and bargaining checklist

This checklist is for an individual or a team to use before an important negotiation, or before designing an assessment scheme or contract. Its four steps correspond to four models from earlier chapters.

  1. Quantify both sides’ BATNAs. Write your own best alternative as a number (not “we have other options”); give the other side’s BATNA as a range rather than a point; from these, work out the zone of possible agreement (ZOPA). Keep in mind the distinction of Chapter 4: a BATNA sets the bottom line, but a fallback that is not good enough may not raise your share. (Chapter 4)
  2. Audit your cost of waiting and the patience your cash flow allows. How much does each month of delay cost you and the other side (cost of capital, idle capacity, a missed season)? Who is in more of a hurry? Can you lower your own cost of waiting before talks start (for example by arranging bridge finance)? (Chapter 4)
  3. Switch from verbal assurances to costly, verifiable signals. List every claim you want the other side to believe, and ask: is there a form of commitment for this claim that is more expensive for “someone saying it falsely” than for “someone saying it truthfully”, and that can be verified and enforced if broken? (Chapter 5)
  4. Red-team the core KPIs for Goodhart leaks. For each key metric in the contract or assessment, ask: what is the cheapest way to push it up a little without creating any real value? Is that cheaper than real improvement? Is the metric checked independently by someone not rewarded on it? (Chapter 6)

Calculation

The checklist applied to a fictional negotiation: a small furniture workshop (A) and a hotel group (B) discuss a one-year supply contract. All numbers are invented, in thousands; an agreement creates a joint surplus of 500.

# Four-step checklist on a FICTIONAL negotiation: a furniture workshop (A) and a hotel
# group (B), one-year supply contract; invented figures in thousands; joint surplus 500.
SURPLUS, bA = 500, 120                   # A's BATNA: sell the capacity elsewhere
print("step 1  BATNAs and the zone of possible agreement (A estimates B's BATNA)")
for bB in (200, 250, 300):
    zopa = SURPLUS - bA - bB
    print(f"  B's BATNA {bB}: ZOPA {zopa}; split the difference: A gets"
          f" {bA + zopa / 2:.0f}")
# Step 2: monthly cost of delay r. With frequent alternating offers A's share of
# the whole surplus tends to rB / (rA + rB); the BATNA binds only if it is larger.
print("step 2  patience audit (B's BATNA 250)")
for label, rA, rB in (("A short of cash", 0.04, 0.01),
                      ("A with bridge loan", 0.01, 0.01)):
    inner = SURPLUS * rB / (rA + rB)
    print(f"  {label:18s}: rA {rA:.2f}, rB {rB:.2f} -> patience share {inner:.0f};"
          f" A gets {max(inner, bA):.0f}")
# Step 3: penalty P if deliveries fail; failure probability 0.05 (reliable) or 0.40
# (unreliable); the contract margin is worth 150 to either type.
MARGIN, p_rel, p_unrel = 150, 0.05, 0.40
print("step 3  penalty clause as a separating signal")
print(f"  unreliable declines if P > {MARGIN / p_unrel:.0f}; reliable signs if"
      f" P < {MARGIN / p_rel:.0f}")
print(f"  P = 400: expected cost reliable {p_rel * 400:.0f},"
      f" unreliable {p_unrel * 400:.0f}")
# Step 4: cost per point to move each KPI honestly vs by gaming; independent check?
kpis = [("on-time, supplier-reported", 5.0, 0.5, False),
        ("on-time, hotel receiving log", 5.0, 6.0, True),
        ("guest complaints about furniture", 8.0, 2.0, False),
        ("defects in random 5 % inspection", 4.0, 9.0, True)]
print("step 4  KPI red team: honest | gaming | independent check")
for name, honest, game, checked in kpis:
    flag = "LEAK" if game < honest and not checked else "ok"
    chk = "yes" if checked else "no"
    print(f"  {name:33s} {honest:4.1f} | {game:4.1f} | {chk:3s} -> {flag}")
# step 1  BATNAs and the zone of possible agreement (A estimates B's BATNA)
#   B's BATNA 200: ZOPA 180; split the difference: A gets 210
#   B's BATNA 250: ZOPA 130; split the difference: A gets 185
#   B's BATNA 300: ZOPA 80; split the difference: A gets 160
# step 2  patience audit (B's BATNA 250)
#   A short of cash   : rA 0.04, rB 0.01 -> patience share 100; A gets 120
#   A with bridge loan: rA 0.01, rB 0.01 -> patience share 250; A gets 250
# step 3  penalty clause as a separating signal
#   unreliable declines if P > 375; reliable signs if P < 3000
#   P = 400: expected cost reliable 20, unreliable 160
# step 4  KPI red team: honest | gaming | independent check
#   on-time, supplier-reported         5.0 |  0.5 | no  -> LEAK
#   on-time, hotel receiving log       5.0 |  6.0 | yes -> ok
#   guest complaints about furniture   8.0 |  2.0 | no  -> LEAK
#   defects in random 5 % inspection   4.0 |  9.0 | yes -> ok

Step 1 shows that the higher A estimates B’s fallback, the narrower the zone of agreement: if B’s BATNA is 250, the zone is 130, and “split the difference” gives A 185. Step 2 switches to alternating-offers reasoning. When A is short of cash and its monthly cost of waiting is four times B’s, patience alone would give A only 100, below its own fallback of 120; the outside option is “activated”, and A gets exactly 120, far less than the 185 of step 1’s split. If A arranges a bridge loan before negotiating so that both sides’ waiting costs are equal, A’s share rises to 250. For A, then, improving patience is worth more than improving the fallback; and steps 1 and 2 use two different models, so A must judge which fits this negotiation better.

Step 3 replaces “we will certainly deliver on time” with a penalty clause. With a penalty above 375, an unreliable supplier (40 % chance of default) would not find it worth signing; as long as it is below 3,000, a reliable supplier (5 % chance of default) would still sign. At a penalty of 400, the reliable supplier’s expected cost is only 20, the unreliable supplier’s 160: this is Chapter 5’s single-crossing condition. Step 4’s red team flags two leaks: on-time delivery reported by the supplier itself, and “guest complaints about furniture”; both are cheaper to game than to improve genuinely, and neither is independently checked. Measured instead through the hotel’s receiving log and random inspections, the leaks disappear.

Note

One fictional negotiation is not evidence. The numbers above only show how the checklist’s calculations work. In real negotiations the other side’s BATNA and cost of waiting can only be estimated, and the estimates themselves are uncertain; the value of the checklist lies in forcing you to write these judgements down so that they can be compared with what happens, not in producing a “correct” answer.

Part 2 A pre-registered dyad-randomised controlled trial

Question

Compared with spending the same time reading standard material on negotiation skills, does spending 10 minutes before a negotiation filling in a structured form (writing down one’s own BATNA and bottom line, estimating the other side’s BATNA, and listing possible trades that create joint gains) increase the joint gain of the two parties in a multi-issue simulated negotiation?

Evidence

Why joint gains are often left on the table. Thompson and Hastie found that most negotiators begin by assuming that the other side’s interests are completely opposed to their own (the “fixed-pie” perception) and often fail to notice issues on which both sides’ interests are identical; those who learn the other side’s interests accurately earlier do better (L. Thompson and Hastie 1990). Thompson and Hrebec’s meta-analysis of 32 experiments called the phenomenon of reaching agreements that are worse for both sides on compatible issues “lose-lose agreements” and discussed its causes (L. Thompson and Hrebec 1996). Thompson’s 1991 experiments found that both providing and seeking information about the other side’s interests improved the accuracy of judgements and led to more integrative agreements, even when only one side did so, and that those who shared information did not lose out (L. L. Thompson 1991). Galinsky and colleagues found that perspective taking helps negotiators discover hidden agreements and raises joint gains (Galinsky et al. 2008). De Dreu, Weingart and Kwon’s meta-analysis of 28 studies found that prosocially motivated negotiators reach higher joint outcomes when resistance to yielding is high, and noted that how studies treat dyads that do not reach agreement affects the conclusions (De Dreu, Weingart, and Kwon 2000). The classic experimental paradigm of integrative bargaining goes back to Pruitt and Lewis (Pruitt and Lewis 1975) and to Raiffa’s treatise (Raiffa 1982).

These studies suggest that structured preparation may help, but none has tested the 10-minute form in this protocol directly. The trial therefore pre-specifies a smallest effect “worth acting on” rather than borrowing an effect size from previous studies.

The negotiation case

The trial uses a five-issue supply-contract case designed for this book, whose structure follows the multi-issue exercises common in published research: two distributive issues (price and delivery date: one side’s gain is the other’s loss), two integrative issues (warranty and payment terms: the two sides value them differently and can trade them) and one compatible issue (packaging standard: both prefer the same option). Each issue has 5 options; each role sees only its own points table; if they fail to agree, each role gets 1,400 points (its BATNA).

Calculation

# Five-issue supply-contract case for the Chapter 8 trial (designed for this book): two
# distributive, two integrative and one compatible issue; 5 options each; BATNA 1,400.
from itertools import product
ISSUES = {                 # points for role A (buyer side), points for role B (supplier)
    "price":         ([0, 300, 600, 900, 1200], [1200, 900, 600, 300, 0]),
    "delivery date": ([0, 200, 400, 600, 800], [800, 600, 400, 200, 0]),
    "warranty":      ([0, 100, 200, 300, 400], [1600, 1200, 800, 400, 0]),
    "payment terms": ([1600, 1200, 800, 400, 0], [0, 100, 200, 300, 400]),
    "packaging":     ([0, 150, 300, 450, 600], [0, 150, 300, 450, 600]),
}
BATNA = 1400
deals = []
for combo in product(range(5), repeat=5):
    a = sum(ISSUES[n][0][k] for n, k in zip(ISSUES, combo))
    b = sum(ISSUES[n][1][k] for n, k in zip(ISSUES, combo))
    deals.append((a + b, a, b, combo))
ok = [d for d in deals if d[1] >= BATNA and d[2] >= BATNA]
best = max(deals)[0]
joint = {d[3]: d[0] for d in deals}
print(f"{len(deals)} possible agreements; {len(ok)} beat both BATNAs")
print(f"maximum joint points {best}: warranty 0, payment terms 0, packaging 4;")
print("  price and delivery only move points between the roles")
print(f"split every issue (2,2,2,2,2): joint {joint[(2, 2, 2, 2, 2)]}")
print(f"trade warranty for payment, split packaging: joint {joint[(2, 2, 0, 0, 2)]}")
top = [d for d in ok if d[0] == best]
print(f"feasible agreements at {best}: {len(top)}; A's points among them "
      f"{min(d[1] for d in top)}-{max(d[1] for d in top)}")
print(f"impasse: joint {2 * BATNA} (sum of BATNAs); outcome range {2 * BATNA}-{best}")
# 3125 possible agreements; 2295 beat both BATNAs
# maximum joint points 6400: warranty 0, payment terms 0, packaging 4;
#   price and delivery only move points between the roles
# split every issue (2,2,2,2,2): joint 4600
# trade warranty for payment, split packaging: joint 5800
# feasible agreements at 6400: 25; A's points among them 2200-4200
# impasse: joint 2800 (sum of BATNAs); outcome range 2800-6400

Of the 3,125 possible agreements, 2,295 are better than the BATNA for both sides. The maximum joint score is 6,400: the warranty option best for B, the payment option best for A, and the packaging option both prefer; price and delivery only move points between the two roles. “Splitting the difference” on every issue yields only 4,600; making the integrative trade but still compromising on the compatible issue yields 5,800, one form of the “lose-lose” outcome. Without agreement the joint score is the sum of the two BATNAs, 2,800.

Design

Element Specification
Participants Adults aged 18 or over, recruited through a university participant pool and community and online advertising, fluent readers of the local working language; not recruited from the author’s community, students, customers or card-deck users, nor from the clients of Asia Influencer X or Yafu Global, the businesses the author founded
Exclusion Having done this case or a closely similar one before; knowing each other within the same session; working as a professional negotiator or procurement agent with systematic negotiation training (not enrolled; if this group is of interest, it is studied in a separate exploratory study)
Pairing and unit of randomisation Participants arriving at the same session are paired at random into dyads of strangers; the dyad is randomised 1:1, stratified by session block; the allocation is revealed from a concealed computer-generated sequence only after pairing; roles (A or B) within the dyad are then assigned at random
Both members get the same condition Both members of a dyad receive the same condition. Reason: the primary outcome is the dyad’s joint gain; treating only one side would mix in the asymmetric effect of “only one side prepared”, which is a different question (Thompson’s 1991 findings suggest it deserves a test of its own, for example a later factorial trial)
Arm A For 10 minutes before negotiating, each member independently fills in the structured form: own BATNA and bottom line; estimated range for the other side’s BATNA; ranking of the issues’ importance to oneself and a guess at their importance to the other side; possible trades and issues on which both sides may agree
Arm B (active control) The same 10 minutes, each member reading standard negotiation-skills material of the same length (general advice such as be confident, listen, make the first offer, do not concede too early), without the structured form
Negotiation Identical in both arms: each member reads the role material and points table privately for 10 minutes, then negotiates face to face for up to 25 minutes, recording the option chosen on each issue on a standard agreement form; pay is a fixed show-up fee plus a bonus proportional to one’s own points
Blinding Participants know there are “two kinds of preparation material” but not the hypothesis; research assistants running sessions only hand out sealed materials and take no part in analysis; the primary outcome is computed automatically from the agreement form, and analysts are blind to arm until unblinding
Primary outcome (single) Dyad joint points: the sum of A’s and B’s points if they agree; the sum of the two BATNAs (2,800) if they reach an impasse. Possible range 2,800–6,400
Secondary outcomes Share of dyads reaching agreement; each role’s own points; whether the maximum joint score of 6,400 is reached; whether a “lose-lose” outcome occurs on the compatible issue; time taken; the Subjective Value Inventory (SVI) (Curhan, Elfenbein, and Xu 2006)
Analysis Intention to treat: all randomised dyads that start negotiating; a linear model with arm as the independent variable and session block as covariate; two-sided α=0.05\alpha = 0.05; pre-specified sensitivity analyses: a rank-based test, and an analysis excluding dyads without agreement (for reference only, never decisive)

Note

Why impasses are scored as the sum of BATNAs. If only dyads that reach agreement were analysed, an intervention that raised both joint gains and the impasse rate would look better than it is; De Dreu and colleagues’ meta-analysis also found that how studies treat dyads without agreement affects the conclusions (De Dreu, Weingart, and Kwon 2000). Scoring an impasse as 2,800 fits the model (without agreement each side really does get its BATNA) and lets the primary outcome reflect both “enlarging the pie” and “talks breaking down”. The agreement rate is reported separately as a secondary outcome.

Sample size

Calculation

# Sample size, dyad-randomised trial; unit = dyad, both members in the same arm.
# A: 10-minute structured preparation form; B: 10 minutes of standard negotiation tips.
# Primary outcome: joint points (impasse = sum of BATNAs), effect in SD units.
# Two-sided alpha 0.05; normal approximation, + 1 per arm.
import math
from statistics import NormalDist
z = NormalDist().inv_cdf

def per_arm(d, power=0.90, alpha=0.05):
    return math.ceil(2 * (z(1 - alpha / 2) + z(power)) ** 2 / d ** 2) + 1

print(" effect (SD) | dyads per arm, 80 % power | 90 % power")
for d in (0.25, 0.30, 0.35, 0.40, 0.50):
    print(f"    {d:.2f}     |           {per_arm(d, 0.80):4d}            |"
          f"    {per_arm(d):4d}")
n = per_arm(0.35)
recruit = math.ceil(n / 0.90)
print(f"chosen: 0.35 SD, 90 % power -> {n} analysable dyads per arm")
print(f"allowing 10 % unusable dyads: randomise {recruit} per arm, {2 * recruit} dyads,"
      f" {4 * recruit} people")
#  effect (SD) | dyads per arm, 80 % power | 90 % power
#     0.25     |            253            |     338
#     0.30     |            176            |     235
#     0.35     |            130            |     173
#     0.40     |            100            |     133
#     0.50     |             64            |      86
# chosen: 0.35 SD, 90 % power -> 173 analysable dyads per arm
# allowing 10 % unusable dyads: randomise 193 per arm, 386 dyads, 772 people

With a smallest effect of interest of 0.35 standard deviations and 90 % power, each arm needs 173 analysable dyads; allowing for about 10 % of dyads being unusable because one member fails to appear or the protocol is breached, each arm randomises 193 dyads, 386 dyads and 772 people in all. If the true effect were only 0.25 standard deviations, each arm would need 338 dyads; this trial does not aim to detect an effect that small.

Decision rule

Calculation

# Decision rule, fixed in advance. d = arm A minus arm B in mean joint points (impasse =
# 2,800) / pooled SD; 95 % CI from the linear model (arm + session block). SESOI 0.35.
SESOI = 0.35

def verdict(d, lo, hi, fidelity_ok, breach):
    if breach:
        return f"d = {d:+.2f}: NOT INTERPRETABLE - concealment or blinding breached"
    if not fidelity_ok:
        return f"d = {d:+.2f}: NOT INTERPRETABLE - < 80 % of arm-A forms as specified"
    if lo >= SESOI:  v = "raises joint gains by at least the smallest effect of interest"
    elif lo > 0:     v = "raises joint gains; size not shown to reach 0.35 SD"
    elif hi < 0:     v = "LOWERS joint gains"
    elif lo >= -SESOI and hi <= SESOI: v = "no difference worth acting on"
    else:            v = "unclear: the interval is too wide to decide"
    return f"d = {d:+.2f} ({lo:+.2f} to {hi:+.2f}): {v}"

for case in ((0.62, 0.41, 0.83, True, False), (0.25, 0.04, 0.46, True, False),
             (0.05, -0.16, 0.26, True, False), (-0.30, -0.51, -0.09, True, False),
             (0.10, -0.25, 0.45, True, False), (0.70, 0.49, 0.91, False, False),
             (0.40, 0.19, 0.61, True, True)):
    print(verdict(*case))
print("secondary (agreement rate, each role's points, SVI): reported with intervals,")
print("never decisive; a rise in impasses is reported prominently whatever d shows")
# d = +0.62 (+0.41 to +0.83): raises joint gains by at least the smallest effect of interest
# d = +0.25 (+0.04 to +0.46): raises joint gains; size not shown to reach 0.35 SD
# d = +0.05 (-0.16 to +0.26): no difference worth acting on
# d = -0.30 (-0.51 to -0.09): LOWERS joint gains
# d = +0.10 (-0.25 to +0.45): unclear: the interval is too wide to decide
# d = +0.70: NOT INTERPRETABLE - < 80 % of arm-A forms as specified
# d = +0.40: NOT INTERPRETABLE - concealment or blinding breached
# secondary (agreement rate, each role's points, SVI): reported with intervals,
# never decisive; a rise in impasses is reported prominently whatever d shows

The example results are invented. If fewer than 80 % of forms in arm A are completed as specified, or allocation concealment or blinding is breached, the report says “not interpretable” whatever the result. Only if the lower limit of the confidence interval for the effect is at least 0.35 standard deviations will the report say “the structured form raised joint gains by at least the smallest effect of interest”. If joint gains rise but impasses also increase, the report must say so prominently.

What this trial cannot show

First, this is a laboratory negotiation with a fixed points table; real business negotiations involve long-term relationships, legal constraints and real money and reputation, and the effect may not carry over. Second, arm A’s form contains three components at once (quantifying one’s BATNA, estimating the other side’s, listing trades); even a positive result cannot say which of them worked. Third, participants from a participant pool may differ greatly from professional negotiators. Fourth, the trial tests only the case where “both sides prepare”; it cannot show what happens when only one side does, nor whether preparation lets one side gain at the other’s expense (each role’s points are reported as a secondary outcome). Fifth, the proportion of integrative and compatible issues in the case is designed; in real negotiations there may be much more value to trade, or much less.

Ethics and conflicts of interest

The trial must be approved by an independent ethics committee; participants give informed consent, and the protocol and analysis plan are registered before the first participants are enrolled (Nosek et al. 2018). No deception is used in the negotiation, and participants know that their pay depends on their own points; anyone may withdraw at any time without giving a reason and still receives the show-up fee.

Disclosure

The author uses the works of 5D Library, including this book, as the methodological basis of his community courses, the 5D Ascension Cards (Dimensional Shift Card Decks) and the Yafu AI knowledge base, and therefore has a commercial interest in the subject of this book. In addition, the author founded and runs Asia Influencer X and Yafu Global, whose day-to-day business involves commercial negotiation and contract design with brands and partners, and he therefore has a direct commercial interest in the subject of this book; the book uses no client data from these businesses, and the Chapter 8 trial does not recruit from their clients. The book promotes no course, card deck or service; the Chapter 8 trial is designed to be run and analysed by researchers independent of the author’s business and does not recruit from the author’s community, students or customers; all the code and the study protocol are published openly for anyone to check. To limit the influence of these interests, the case materials, the form and the analysis code are made public before enrolment, and the results, data and code will be published whatever the outcome.

References

Curhan, Jared R., Hillary Anger Elfenbein, and Heng Xu. 2006. “What Do People Value When They Negotiate? Mapping the Domain of Subjective Value in Negotiation.” Journal of Personality and Social Psychology 91 (3): 493–512. https://doi.org/10.1037/0022-3514.91.3.493.
De Dreu, Carsten K. W., Laurie R. Weingart, and Seungwoo Kwon. 2000. “Influence of Social Motives on Integrative Negotiation: A Meta-Analytic Review and Test of Two Theories.” Journal of Personality and Social Psychology 78 (5): 889–905. https://doi.org/10.1037/0022-3514.78.5.889.
Galinsky, Adam D., William W. Maddux, Debra Gilin, and Judith B. White. 2008. “Why It Pays to Get Inside the Head of Your Opponent: The Differential Effects of Perspective Taking and Empathy in Negotiations.” Psychological Science 19 (4): 378–84. https://doi.org/10.1111/j.1467-9280.2008.02096.x.
Nosek, Brian A., Charles R. Ebersole, Alexander C. DeHaven, and David T. Mellor. 2018. “The Preregistration Revolution.” Proceedings of the National Academy of Sciences 115 (11): 2600–2606. https://doi.org/10.1073/pnas.1708274114.
Pruitt, Dean G., and Steven A. Lewis. 1975. “Development of Integrative Solutions in Bilateral Negotiation.” Journal of Personality and Social Psychology 31 (4): 621–33.
Raiffa, Howard. 1982. The Art and Science of Negotiation. Cambridge, MA: Belknap Press of Harvard University Press.
Thompson, Leigh L. 1991. “Information Exchange in Negotiation.” Journal of Experimental Social Psychology 27 (2): 161–79. https://doi.org/10.1016/0022-1031(91)90020-7.
Thompson, Leigh, and Reid Hastie. 1990. “Social Perception in Negotiation.” Organizational Behavior and Human Decision Processes 47 (1): 98–123. https://doi.org/10.1016/0749-5978(90)90048-E.
Thompson, Leigh, and Dennis Hrebec. 1996. “Lose-Lose Agreements in Interdependent Decision Making.” Psychological Bulletin 120 (3): 396–409. https://doi.org/10.1037/0033-2909.120.3.396.

Fan, Y. (2026). Mechanism Design, Incentive Compatibility and the Game Theory of Negotiation: From Vickrey Auctions and the Myerson-Satterthwaite Theorem to Nash Bargaining, Read Beside Classical Chinese Legalist and Confucian Institutional Thought [机制设计、激励相容与谈判博弈的数学模型] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23765012 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).