PD — Prisoner’s Dilemma

GT Behaviour · GTEMO Experiment

TipPayoff matrix — Row payoff, Column payoff

	T (col)	D (col)
T (row)	18, 18 ♦	0, 22
D (row)	22, 0	8, 8 ★

★ = Nash equilibrium (dominant strategy). ♦ = Pareto optimum. D strictly dominates T for both players: the unique Nash equilibrium (D, D) = 8/8€ is Pareto-inferior to mutual cooperation (T, T) = 18/18€. Cheap talk may shift cooperation toward the Pareto-optimal outcome.

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1 — Equilibria & coordination

Objective

Describe the equilibrium outcomes reached by each couple in Part 1 and Part 2, and test whether cheap talk shifted coordination rates using paired McNemar tests.

TipEquilibrium labels (PD)

• Coop-Coop (T,T) — Pareto-optimal; both cooperate ♦
• Nash (D,D) — Nash equilibrium; both defect ★

Equilibrium distributions

p_eq_pd

Figure 1: PD — Equilibrium distributions in Part 1 (top) and Part 2 (bottom).

Coordination rates: Part 1 vs Part 2

coord_pd |>
  dplyr::select(part, x, n, pct, ci95) |>
  gt::gt() |>
  gt::tab_header(title    = "PD — Coordination rates: Part 1 vs Part 2",
                 subtitle = "95% Clopper-Pearson CI") |>
  gt::cols_label(part = "Phase", x = "n coordinated", n = "N",
                 pct = "%", ci95 = "95% CI") |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_column_labels())
p_coord_pd

PD — Coordination rates: Part 1 vs Part 2
95% Clopper-Pearson CI
Phase	n coordinated	N	%	95% CI
Part 1	2	14	14.3%	[1.8%, 42.8%]
Part 2	6	14	42.9%	[17.7%, 71.1%]

Figure 2: PD — Coordination rate in Part 1 vs Part 2 (couple level). 95% Clopper-Pearson CI.

McNemar tests

tab_mc_pd |>
  gt::gt() |>
  gt::tab_header(title    = "McNemar tests — PD (couple level)",
                 subtitle = "Paired Part 1 vs Part 2") |>
  gt::cols_label(label = "Test", statistic = "χ²", p_value = "p-value",
                 note = "Note") |>
  gt::fmt_number(columns = c(statistic, p_value), decimals = 4, rows = !is.na(statistic)) |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_body(columns = p_value,
                                           rows = !is.na(p_value) & p_value < 0.05)) |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_column_labels())

McNemar tests — PD (couple level)
Paired Part 1 vs Part 2
Test	χ²	p-value	Note
PD — coord Part1 vs Part2	1.1250	0.2888	OK
PD — mutual cooperation Part1 vs Part2	0.8000	0.3711	OK

Note

Mutual cooperation (T, T) in Part 1: 35.7% of pairs → Part 2: 14.3%. A significant McNemar result would indicate that cheap talk systematically elevated mutual cooperation above the Nash equilibrium level.

Conditioning on session gender

tab_cond_coord_pd |>
  gt::gt() |>
  gt::tab_header(title    = "PD — Coordination and cooperation by session gender",
                 subtitle = "χ² with Monte Carlo simulated p-value (B = 2000), couple level") |>
  gt::cols_label(Outcome = "Outcome", Factor = "Factor", Test = "χ²(sim.) test") |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_column_labels()) |>
  gt::opt_stylize(style = 1) |>
  gt::tab_options(table.font.size = 13)
p_coord_gender_pd

PD — Coordination and cooperation by session gender
χ² with Monte Carlo simulated p-value (B = 2000), couple level
Outcome	Factor	χ²(sim.) test
Coordination Part 2	Session gender	χ²(sim.): p = 0.270 ns
Coordination Part 1	Session gender	χ²(sim.): p = 0.468 ns
Mutual cooperation Part 2	Session gender	χ²(sim.): p = 0.464 ns
Mutual cooperation Part 1	Session gender	χ²(sim.): p = 1.000 ns

Figure 3: PD — P(Coordination Part 2) by session gender (couple level). Error bars = 95% Clopper-Pearson CI.

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2 — Choice & signal distributions

Objective

Describe the marginal distributions of choices and signals (Part 1 choice → signal sent → Part 2 choice), and examine how the opponent’s signal shapes Part 2 behaviour. All proportions use exact 95% Clopper-Pearson CIs.

Distributions table

tab_pd

PD — Choice and signal distributions
95% Clopper-Pearson CI
Choice / Signal	n	N	%	95% CI
Part 1
T	17	28	60.7%	[40.6%, 78.5%]
D	11	28	39.3%	[21.5%, 59.4%]
Signal
T	17	28	60.7%	[40.6%, 78.5%]
D	11	28	39.3%	[21.5%, 59.4%]
Part 2
T	10	28	35.7%	[18.6%, 55.9%]
D	18	28	64.3%	[44.1%, 81.4%]

Proportions by phase

p_pd_dist

Figure 4: PD — Proportions of each choice/signal type with 95% Clopper-Pearson CIs. Left: Part 1 choices; centre: signals sent; right: Part 2 choices.

NotePart 1 → Part 2 snapshot

Cooperation (T) in Part 1: 60.7%. The dominant signal was T (60.7%). Cooperation in Part 2: 35.7%. An increase in T from Part 1 to Part 2 would be consistent with cheap talk successfully promoting Pareto-improving coordination despite the dominance of defection.

Within-subject shift: McNemar test (Part 1 vs Part 2)

tab_mcnemar_pd |>
  gt::gt() |>
  gt::tab_header(
    title    = "McNemar test — PD: cooperated_part1 vs cooperated_part2",
    subtitle = "Paired within-individual"
  ) |>
  gt::cols_label(statistic = "χ²", p_value = "p-value", n = "n", note = "Note") |>
  gt::fmt_number(columns = c(statistic, p_value), decimals = 4) |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_body(columns = p_value,
                                           rows = !is.na(p_value) & p_value < 0.05)) |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_column_labels())

McNemar test — PD: cooperated_part1 vs cooperated_part2
Paired within-individual
χ²	p-value	n	Note
2.7690	0.0961	28	OK

Note

A significant McNemar result (p < 0.05) indicates that pre-play cheap talk systematically shifted individual cooperation rates — consistent with the hypothesis that signals influence behaviour even in PD where defection is the dominant strategy.

Opponent signal and the information set before Part 2

Important

Decision sequence. After sending their own signal and before making the Part 2 choice, each player observes the opponent’s signal. The Part 2 decision is taken with a two-dimensional information set: (own signal sent) × (opponent’s signal received). The four possible information sets are: T/T, T/D, D/T, D/D.

p_sig_heatmap_pd

Figure 5: PD — Joint distribution of own signal × opponent signal received. Values show count and share.

p_choice2_by_oppsig_pd

Figure 6: PD — P(choice₂ = T) stratified by opponent’s signal. 95% Clopper-Pearson CI.

NoteCheap talk in PD: signal has no credible effect on Part 2 behaviour

In the Prisoner’s Dilemma, defection (D) is the dominant strategy for both players, regardless of what the opponent signals. The near-identical cooperation rates — 35.3% when the opponent signals T vs 36.4% when the opponent signals D — confirm this theoretical prediction. The opponent’s signal cannot credibly promote cooperation because D strictly dominates T at any belief about the opponent’s choice. This means: (1) when the opponent signals T (intending cooperation), many still defect (64.7%) because they rationally distrust the signal; and (2) when the opponent signals D, some still cooperate (36.4%) — not out of strategic response, but likely due to social preferences, altruism, or misunderstanding the game. The absence of a signal effect contrasts sharply with Stag Hunt, where mutual cooperation is an equilibrium: there, cheap talk meaningfully shifts behaviour (55.6% when opp signals T vs 30.4% when opp signals D), because the signal can be credible.

p_choice2_infoset_pd

Figure 7: PD — P(choice₂ = T) by full information set (own/opp). Colour = own signal. 95% CI. Information sets with no observations are omitted.

NotePD interpretation

The critical test is the (T/T) information set — where both players have promised cooperation. Even here, full cooperation in Part 2 may fall well below 100%, consistent with the theoretical prediction that cheap talk is non-binding and strategic distrust persists. When the opponent signals D, cooperation typically falls further.

p_follow_opp_pd

Figure 8: PD — Proportion of players whose Part 2 choice matches the opponent’s signal received.

Conditioning on gender and role

tab_cond_sig_pd |>
  gt::gt() |>
  gt::tab_header(title = "PD — Choice and signal distributions by gender and role",
                 subtitle = "χ² with Monte Carlo simulated p-value (B = 2000)") |>
  gt::cols_label(Outcome = "Outcome", Factor = "Factor", Test = "χ²(sim.) test") |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_column_labels()) |>
  gt::opt_stylize(style = 1) |>
  gt::tab_options(table.font.size = 13)

PD — Choice and signal distributions by gender and role
χ² with Monte Carlo simulated p-value (B = 2000)
Outcome	Factor	χ²(sim.) test
Part 1 = T	Gender	χ²(sim.): p = 0.695 ns
Part 1 = T	Role	χ²(sim.): p = 0.428 ns
Signal = T	Gender	χ²(sim.): p = 1.000 ns
Signal = T	Role	χ²(sim.): p = 0.422 ns
Part 2 = T	Gender	χ²(sim.): p = 0.108 ns
Part 2 = T	Role	χ²(sim.): p = 0.698 ns

p_cond_sig_pd

Figure 9: PD — P(Signal = T) by gender and role. Error bars = 95% Clopper-Pearson CI. Dashed line = 50%.

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3 — Signal honesty & consistency

Objective

Examine whether signals are honest (= same as the action eventually taken in Part 2) and consistent with Part 1 choices. Assess the prevalence of strategy switches between Part 1 and Part 2.

Honesty and consistency proportions

tab_sec2_pd |>
  gt::gt() |>
  gt::tab_header(title    = "PD — Signal honesty and consistency",
                 subtitle = "95% Clopper-Pearson CI. Each row is a binary indicator (1 = yes, 0 = no).") |>
  gt::cols_label(variable = "Measure", n = "n (=1)", N = "N",
                 pct = "%", ci95 = "95% CI") |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_column_labels()) |>
  gt::tab_footnote(
    footnote = "1 if the signal sent equals the Part 2 choice (e.g. sent T and chose T in Part 2). Measures whether players followed through on their signal.",
    locations = gt::cells_body(columns = variable, rows = 1)
  ) |>
  gt::tab_footnote(
    footnote = "1 if the signal sent equals the Part 1 choice (e.g. signalled T and had also chosen T in Part 1). Measures whether the signal reflects past behaviour — independent of Part 2.",
    locations = gt::cells_body(columns = variable, rows = 2)
  ) |>
  gt::tab_footnote(
    footnote = "1 if the Part 2 choice differs from the Part 1 choice (choice1 \u2260 choice2). Measures switching behaviour across rounds, independent of the signal. N may differ from rows 1\u20132 due to missing values in different variables.",
    locations = gt::cells_body(columns = variable, rows = 3)
  ) |>
  gt::tab_options(table.font.size = 13)

PD — Signal honesty and consistency
95% Clopper-Pearson CI. Each row is a binary indicator (1 = yes, 0 = no).
Measure	n (=1)	N	%	95% CI
Signal honest (signal = choice2)1	15	28	53.6%	[33.9%, 72.5%]
Signal consistent with Part 1 (signal = choice1)2	14	28	50.0%	[30.6%, 69.4%]
Strategy changed Part 1 → Part 2 (choice1 ≠ choice2)3	13	28	46.4%	[27.5%, 66.1%]
1 1 if the signal sent equals the Part 2 choice (e.g. sent T and chose T in Part 2). Measures whether players followed through on their signal.
2 1 if the signal sent equals the Part 1 choice (e.g. signalled T and had also chosen T in Part 1). Measures whether the signal reflects past behaviour — independent of Part 2.
3 1 if the Part 2 choice differs from the Part 1 choice (choice1 ≠ choice2). Measures switching behaviour across rounds, independent of the signal. N may differ from rows 1–2 due to missing values in different variables.

Binomial test: signal honesty vs 50%

tab_binom_honest_pd |>
  gt::gt() |>
  gt::tab_header(title    = "Binomial test: P(Honest) vs H₀ = 0.50",
                 subtitle = "Two-sided test; 95% Clopper-Pearson CI") |>
  gt::cols_label(x = "n honest", n = "N", pct = "%", ci95 = "95% CI",
                 p_value = "p-value") |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_body(columns = p_value,
                                           rows = p_value < 0.05)) |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_column_labels())

Binomial test: P(Honest) vs H₀ = 0.50
Two-sided test; 95% Clopper-Pearson CI
n honest	N	%	95% CI	p-value
15	28	53.6%	[33.9%, 72.5%]	0.8506

Note

In PD, a signal is honest if the player’s Part 2 action matches what they signalled. The aggregate honesty rate must be interpreted with caution: honesty is only behaviorally meaningful for T signals. A player who signals D and then defects is simply playing the dominant strategy — their “honesty” would have occurred regardless of the signal. By contrast, a player who signals T and then cooperates is making a costly choice (forgoing the defection payoff), so P(choice2 = T | signal = T) is the relevant measure of credible cheap talk. The overall honesty rate conflates these two very different cases and tends to be inflated by the trivially honest D→D cases.

Strategic transition heatmaps

p_sankey_pd

Figure 10: PD — Strategic transitions. Left: Part 1 → Signal (row %: conditional on Part 1 choice). Right: Signal → Part 2 (row %: conditional on signal sent).

Conditioning on gender and role

tab_cond_honest_pd |>
  gt::gt() |>
  gt::tab_header(title    = "PD — Signal honesty and strategy change by gender and role",
                 subtitle = "χ² with Monte Carlo simulated p-value (B = 2000)") |>
  gt::cols_label(Outcome = "Outcome", Factor = "Factor", Test = "χ²(sim.) test") |>
  gt::tab_style(style = gt::cell_text(weight = "bold"),
                locations = gt::cells_column_labels()) |>
  gt::opt_stylize(style = 1) |>
  gt::tab_options(table.font.size = 13)

PD — Signal honesty and strategy change by gender and role
χ² with Monte Carlo simulated p-value (B = 2000)
Outcome	Factor	χ²(sim.) test
Signal honest	Gender	χ²(sim.): p = 0.457 ns
Signal honest	Role	χ²(sim.): p = 0.456 ns
Strategy changed	Gender	χ²(sim.): p = 1.000 ns
Strategy changed	Role	χ²(sim.): p = 0.454 ns

p_cond_honest_pd

Figure 11: PD — P(Honest) by gender (left) and role (right). Error bars = 95% Clopper-Pearson CI. Dashed line = 50%.

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4 — Belief accuracy & bonus

NoteThe two belief questions

After Part 2, each player answered two incentivised questions about their beliefs:

Belief 1 — First-order belief: “What do you think your opponent chose in Part 2?” (T or D). Scored correct (GT_right_guess1 = 1) if the player’s prediction matched the opponent’s actual Part 2 choice. Bonus: +2€ if correct.

Belief 2 — Second-order belief: “What do you think your opponent believes you chose in Part 2?” (T or D). Scored correct (GT_right_guess2 = 1) if the player correctly identified what the opponent believed about the player’s own choice. Bonus: +2€ if correct.

The belief accuracy score = GT_right_guess1 + GT_right_guess2 ∈ {0, 1, 2}. The belief bonus = score × 2€ ∈ {0€, 2€, 4€}.

Objective

Describe the distribution of belief accuracy scores (0 = both beliefs wrong; 1 = one correct; 2 = both correct) and the associated belief bonus payoff. Assess whether belief accuracy is correlated with coordination outcomes at the couple level.

Belief accuracy distribution

p_belief_bar_pd

Figure 12: PD — Distribution of belief accuracy scores.

Hypothesis tests: beliefs, cognitive ability & coordination

PD — Belief accuracy: hypothesis comparison
H1–H2: individual level. H3: couple level. Stat = Spearman ρ or φ (phi).
	Level	Hypothesis	X	Y	Test	Expected	Stat	p	n
H1	Individual	Reflective thinkers (high CRT) predict opponent’s choice more accurately	CRT score (0–4)	Belief accuracy (0–2)	Spearman ρ	Positive	0.041	0.835	28
H2	Individual	Players who made more quiz errors have less accurate beliefs	Quiz errors [log(1+x)]	Belief accuracy (0–2)	Spearman ρ	Negative	-0.097	0.623	28
H3	Couple	Couples where both players have perfect beliefs coordinate more in Part 2	Coord. Part 2 (0/1)	Both perfect beliefs (0/1)	Fisher exact + φ1	Positive	0.059	1.000	14
1 H3 stat = phi coefficient (φ); p-value from two-sided Fisher exact test on 2×2 contingency table.

Note

H1 tests whether more reflective players (higher CRT) are better at predicting their opponent — if strategic reasoning drives belief formation, a positive Spearman ρ is expected. H2 tests whether players who struggled with game comprehension (more quiz errors) hold less accurate beliefs — expected direction is negative. H3 tests whether couples where both players had perfect beliefs were more likely to coordinate in Part 2 — the only couple-level hypothesis; uses Fisher exact given small N and binary outcomes. Note that H1 and H2 operate at the individual level while H3 is at the couple level; they are not directly comparable.

Conditioning on gender and role

p_cond_belief_pd

Figure 13: PD — Belief accuracy score (0/1/2) by gender (left) and role (right). Bars show proportion within each group; labels show % and count. Score 0 = both beliefs wrong, 1 = one correct, 2 = both correct.

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5 — Econometric models

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5.1 — Determinants of belief accuracy

Estimate an ordered logit (proportional-odds model) for the belief accuracy score (0 = both wrong, 1 = one correct, 2 = both correct) using Theory of Mind (MASC) and IRI subscales as predictors. The proportional-odds assumption implies a single log-odds shift per unit increase in each predictor, shared across both thresholds (0→1 and 1→2).

WarningSmall-sample caveat

With n = 28 participants (score 0: n=6; 1: n=13; 2: n=9), EPV is computed as min(n₀, n₂) / k: M1 = 6, M2 = 3, M3 = 2. All are well below the recommended 10. All results are exploratory and should be treated as hypothesis-generating.

Model specifications

\[ \begin{aligned} \text{M1:} \quad & \text{logit}\,P(Y \le j) = \alpha_j - \beta_1\,\text{MASC}_z \\ \text{M2:} \quad & \text{logit}\,P(Y \le j) = \alpha_j - \beta_1\,\text{MASC}_z - \beta_2\,\text{IRI-PT}_z \\ \text{M3:} \quad & \text{logit}\,P(Y \le j) = \alpha_j - \beta_1\,\text{MASC}_z - \beta_2\,\text{IRI-PT}_z - \beta_3\,\text{IRI-PD}_z \end{aligned} \]

MASC = Theory of Mind total score; IRI-PT = Perspective Taking subscale (cognitive empathy — most directly linked to predicting opponents’ decisions); IRI-PD = Personal Distress subscale (self-oriented distress — may impair strategic prediction). All scores z-standardised. OR > 1 shifts probability towards higher belief accuracy.

Coefficient table

tab_olog_gt

PD — Ordered logit: determinants of belief accuracy
DV = belief accuracy score (0/1/2, ordered). n = 28 (score 0: n=6; 1: n=13; 2: n=9). MASC/IRI z-scored. OR > 1 increases probability of higher accuracy.1
Predictor	β	SE	t	p	OR	OR 2.5%	OR 97.5%
M1: MASC only
MASC ToM score (z)	-0.124	0.371	-0.334	0.7385	0.883	0.427	1.828
M2: MASC + IRI-PT
MASC ToM score (z)	-0.079	0.386	-0.205	0.8372	0.924	0.428	1.988
IRI Perspective Taking (z)	-0.164	0.374	-0.439	0.6610	0.849	0.399	1.773
M3: MASC + IRI-PT + IRI-PD
MASC ToM score (z)	-0.063	0.399	-0.157	0.8752	0.939	0.424	2.077
IRI Perspective Taking (z)	-0.158	0.376	-0.419	0.6749	0.854	0.400	1.801
IRI Personal Distress (z)	0.056	0.350	0.160	0.8727	1.058	0.529	2.140
1 Ordered logit (proportional-odds, MASS::polr). p-values from two-tailed z-test on t-statistic. CI from profile likelihood where convergent, otherwise Wald. All models MLE; EPV < 10 — interpret cautiously.

Goodness of fit

tab_gof_olog_gt

PD — Ordered logit: goodness of fit
DV = belief accuracy score (0/1/2). EPV = min(n₀, n₂) / k.
Model	n	Predictors	EPV	AIC	McFadden R²
M1: MASC only	28	1	6	64.8	0.0019
M2: MASC + IRI-PT	28	2	3	66.6	0.0052
M3: MASC + IRI-PT + IRI-PD	28	3	2	68.5	0.0056

Forest plot: odds ratios

p_forest_olog

Figure 14: PD — Ordered logit: odds ratios for belief accuracy. OR > 1 increases probability of higher accuracy score. Error bars = 95% CI. Dashed line = OR 1 (no effect). x-axis log scale.

NoteInterpretation

MASC ToM (M1–M3): OR = 0.883, p = 0.7385. Higher Theory of Mind ability may improve belief accuracy by enabling better prediction of opponents’ decisions — an OR > 1 is consistent with this interpretation. IRI Perspective Taking (M2–M3): OR = 0.849, p = 0.661 — cognitive empathy is directly relevant to inferring opponents’ intended strategies; a positive OR would support the link between perspective-taking and prediction accuracy. IRI Personal Distress (M3): OR = 1.058, p = 0.8727 — self-oriented distress may interfere with accurate belief formation (OR < 1 expected). Given EPV ≤ 6 across all models, all estimates carry substantial uncertainty.

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5.2 — Cooperation under defection signal

WarningSmall-sample note

This analysis restricts the sample to participants who received a D signal from their opponent (opp_signal_received = D). The dependent variable is whether they nonetheless chose T (cooperate). Given the small subsample size, EPV may be below 10 and Firth penalised logit is applied automatically.

Models

\[ \begin{aligned} \text{M1:} \quad & \text{logit}\,P(T) = \beta_0 + \beta_1\,\text{quiz\_err} \\ \text{M2:} \quad & \text{logit}\,P(T) = \beta_0 + \beta_1\,\text{quiz\_err} + \beta_2\,\text{CRT} \\ \text{M3:} \quad & \text{logit}\,P(T) = \beta_0 + \beta_1\,\text{CRT} \end{aligned} \]

Sample: opp_signal_received = D only. n = 11, events = 4. EPV: M1 = 4, M2 = 2, M3 = 4. All estimated with Firth penalised logit.

Results

PD — Cooperation when opponent signals D
DV = choice2=T | opp_signal=D. n=11, events=4. EPV: M1=4, M2=2, M3=4. All Firth penalised logit (brglm2).1
Predictor	β	SE	z	p	OR	OR 2.5%	OR 97.5%
M1: Quiz only
Quiz errors [log(1+x)]	1.028	0.646	1.59	0.112	2.79	0.79	9.91
M2: Quiz + CRT
Quiz errors [log(1+x)]	0.957	0.785	1.22	0.223	2.60	0.56	12.13
CRT score (0–4)	-0.010	0.830	-0.01	0.991	0.99	0.19	5.03
M3: CRT only
CRT score (0–4)	0.696	0.698	1.00	0.319	2.01	0.51	7.87
1 Firth penalised logit used for all models (EPV < 10). OR > 1 → increases P(cooperate | opp signals D). 95% Wald CI.

Figure 15: Cooperation when opponent signals D — M1 (quiz only), M2 (quiz + CRT), M3 (CRT only). Odds ratios with 95% CI. OR > 1 increases P(cooperate). All Firth. x-axis log scale.

NoteInterpretation

Quiz errors (OR = 2.6, p = 0.223): a higher error rate on the comprehension quiz may reflect lower understanding of the game, potentially increasing naive cooperation even after a D signal. CRT score (OR = 0.99, p = 0.991): more reflective thinkers may be more sensitive to the dominant strategy argument and less likely to cooperate when signalled D. EPV = 2 — estimates are exploratory and should be interpreted with caution.