In The Speed of Trust, Steven M.R. Covey argues that trust is monetizable. This study confirms Covey's hypothesis by applying binary classification (via SAS Proc Logistic) to 10 years of data from a 3 x 3 prisoner's dilemma game.

1. Advisors Dr. Jennifer Lewis Priestley & Dr. Brad Barney
Department of Statistics & Analytical Sciences
ABSTRACT
Binary logistic regression was used to test the association of early-round bidding
strategies with profit and counterparty trust outcomes for teams of players in a
simultaneous, 8-round (“iterated”) 3x3 prisoner’s dilemma game. Data were
obtained between 2006 and 2015 from KSU grad and undergrad accounting and
business law courses (n=222). Research questions were whether bids in rounds 1-
6 affected (a) the trust of counterparties in the game’s crucial rounds 7 and 8 or (b)
total team profits. If yes to either (a) or (b), which bidding strategies were most
likely to maximize profits and trust? Main effects of bids (own and counterparty),
course, and year were statistically significant, suggesting that bidding strategies
did (and do) affect both profits and counterparty trust in contract settings and that
trust and profits may enjoy a symbiotic relationship.
INTRODUCTION
METHODS & FINDINGS
CONCLUSION
Game Theory & Logistic Regression:
Monetizing Trust in Contracts Through Binary Classification
Kurt S. Schulzke
Figure 2 – Specimen game results by round
In The Speed of Trust, Steven M.R. Covey argues that trust is monetizable, an
hypothesis on which the OPEC oil cartel has banked for decades. Yet, as recent
cartel history demonstrates, trust among counterparties is easily lost and difficult to
recover. The same can be said of the trust on which all business contracts are built.
Contracts and their trust foundation can be modeled by matrix games. The Oil
Pricing Exercise, a prisoner’s dilemma game published by the Harvard Program on
Negotiation (see payoff matrix in Figure 1) was used to generate data.
Each observation represents eight rounds of bidding (roughly 3 min./round) by a
pair of team counterparties in a classroom with up to 5 other pairs also bidding
against each other. In each round, each team bids simultaneously (prior to learning
the counterparty bid). After receiving all bids for a round, the facilitator shows all
bids and payoffs for that round (see, e.g., Figure 2) to all participants.
For the first 3 rounds, counterparty identities (but not bids) are cloaked. Prior to
bidding in Round 4 (for which payoffs are doubled), counterparty identities are
disclosed and sides allowed to negotiate briefly (5 min.) with each other through a
single representative on each side. Rounds 5 and 6 revert to original rules. Prior to
Round 7, sides are again allowed to negotiate, understanding that in Rounds 7 and
8 the payoff for that round’s high-score counterparty, if any, will be quadrupled.
Bidding “10” is the dominant game theoretic or “rational” strategy in every round.
Conversely, in most rounds, a bid of 30 signals highest trust, with alternating 30
and 20 bids, being most trusting and cooperative in Rounds 7 and 8.
Binary proxy variables for profits and trust were as follows:
Profits: OptP = 1, if total team profits > 120 (80% of pareto optimal profit of
151), else 0. Freq = 103/222.
Trust: OpTrust78 = 1, if counterparty alternates bids of 30 and 20 in Rounds 7
and 8, else 0. Freq = 92/222.
Predictors for each model are reflected in the SAS Proc Logistic output in the
middle panel.
Narrowly speaking, the findings answer “yes” to research questions (a) and (b)
and, as to (c), they encourage game-theory-defying high bids in Rounds 1 and 4 of
the Oil Pricing Exercise, if a team wishes to accumulate profit in excess of 80
percent of the pareto-optimal 151 or to engender maximum counterparty trust in
Rounds 7 and 8.
Additionally, the odds favored Years 2006 and 2015 and BLAW 8340 and BLAW
3400. BLAW 3400’s advantage over BLAW 8340 may indicate that MBA students
tend to be more competitive and less cooperative than undergrad negotiation
students, who come from a more academically diverse population. BLAW 2200’s
consistently low performance defies easy explanation and invites further
investigation.
More broadly, the findings suggest that playing contracts by the game theory book
may lead to lower profits than irrationally engaging in risky, trusting behavior with
unpredictable counterparties. Finally, the evidence offered here supports Steven
M.R. Covey’s assertion that trust and money run together.
Figure 1 – Base game payoff matrix
Bids by Round
Table Alba Batia Alba Batia Alba Batia Alba Batia Alba Batia Alba Batia Alba Batia Alba Batia
A 10 10 10 10 10 20 30 30 30 20 20 30 20 20 10 10
B 10 10 10 10 10 10 30 10 10 10 30 10 20 30 10 20
C 20 10 10 10 10 20 30 30 30 30 30 30 20 30 30 20
D 30 10 10 30 30 30 30 30 30 30 30 30 10 30 10 10
Optimal 30 30 30 30 30 30 30 30 30 30 30 30 30 20 20 30
Total Profits
Profits by Round Yellow Blue
A 5 5 5 5 15 3 22 22 2 18 18 2 8 8 5 5 80 68
B 5 5 5 5 5 5 4 30 5 5 2 15 72 2 60 3 158 70
C 3 15 5 5 15 3 22 22 11 11 11 11 72 2 2 72 141 141
D 2 15 15 2 11 11 22 22 11 11 11 11 60 2 5 5 137 79
Optimal 11 11 11 11 11 11 22 22 11 11 11 11 2 72 72 2 151 151
7 81 2 3 4 5 6
Profit Model Trust Model
Student preparation for games varied by year and course, with more robust
orientation regarding basic game theory and dynamics of the Oil Pricing Exercise
offered in BLAW 8340 and 3400, both negotiation courses. Usually, course grade
was tied to team profit. Teams comprised between 2 and 5 members.
Proc Logistic was used to train Profit and Trust models to the resulting bid and
profit data. Predictors were selected through backward elimination. Diagnostic
plots (e.g., Figures 3-4) pinpointed influential outliers (obs 2 & 220 for Profit; 113
& 145 for Trust) which were excluded for Proc Logistic cross-validation (see SAS
Usage Note 39724) used in place of separate training and validation sets because
data were scarce.
Figure 3 – Profit Model Figure 4 – Trust Model
All results shown, except Figures 3 and 4, are for cross-validated Profit and Trust
models both globally significant at alpha=.05 with ROC 95% CIs that exclude 0.
Comparative ROC plots (top left/right, center panel) show c-stat shrinkage ≈ 10
and 12 percent (Model vs ROC1) for Profit and Trust, respectively, but c stats (0.68
and 0.66) reflect significant retained predictive power. Gains and lift panels
(left/right of center, bottom) suggest that greatest lift is provided by the top three
(two) deciles for the Profit (Trust) model.
Odds ratio estimates, 95% CIs (immediate left), and Type 3 tests show Own1,
Opp1, and Own4 bids significant in both models, while the models flipped Own
and Opp in rounds 2 and 6, in which the odds in both models favor low bids but
high Own1, Opp1, and Own4 bids. This is consistent with the eight Predicted Prob
x Predictor plots (center panel, last four rows).
In both models, Year and Course were significant with BLAW 8340 (MBA
negotiation) fairing well vs all but BLAW 3400 (undergrad negotiation) and 2015
beating all but 2006. Standardized betas indicate that bidding strategies in Rounds
1, 4 and 6 were relatively impactful for both trust and profits.
Prices 30 20 10
11 18 15
30 11 2 2
2 8 15
20 18 8 3
2 3 5
10
15 15 5
RowPlayer
Column Player