Experiment report: collusion_screens
A bid-rotation cartel of five agents (designated winner bids cost x1.6, others cover at x2.2) against an otherwise competitive market. Measures buyer cost and two simple screens from the procurement literature: the coefficient of variation of bids per auction and the relative distance between the two lowest bids.
Hypothesis
The cartel raises average buyer cost; the screens move (higher relative distance between the two lowest bids) when it is present.
Experimental setup
- Replications: 30 per arm (common random numbers across arms)
- Seed: 31
- AuctionSI 0.1.1, Python 3.12.15, git commit 0162c05e54894a8575355e5fb4d3f5d47dd18a08
- Baseline arm:
competitive
- Confidence level: 95%; alpha: 0.05
Parameters
- Agents: {'count': 12, 'capabilities': ['general'], 'capability_distribution': 'mixed', 'capabilities_per_agent': (1, 1), 'cost_distribution': 'lognormal', 'variable_cost_ratio': 0.01, 'quality_distribution': 'beta', 'quality_spread': 0.05, 'latency_distribution': 'lognormal', 'reliability_distribution': 'beta', 'capacity_distribution': 1, 'strategy': 'cost_plus', 'quality_report_bias': 0.0}
- Tasks: {'count': 400, 'task_types': ['general'], 'arrival_rate': 1.0, 'budget_distribution': 'lognormal', 'deadline_distribution': 'uniform', 'complexity_distribution': 'lognormal', 'min_quality': None, 'value_multiplier': 1.5}
- Defaults: mechanism=first_price_reverse, policy=lowest_price, reputation=multi_dimensional, settlement=pay_on_pass
Arms
competitive: experiment defaultscartel: {'environment': {'adversaries': {'colluders': 5, 'winner_markup': 0.6, 'cover_markup': 1.2}}}
Results
average_cost
| arm |
n |
mean |
95% CI |
sd |
median |
| competitive |
30 |
0.04053 |
[0.03845, 0.04261] |
0.005575 |
0.04114 |
| cartel |
30 |
0.04844 |
[0.04595, 0.05092] |
0.006649 |
0.04848 |
bid_cv
| arm |
n |
mean |
95% CI |
sd |
median |
| competitive |
30 |
0.3123 |
[0.2836, 0.341] |
0.07686 |
0.3129 |
| cartel |
30 |
0.3181 |
[0.2932, 0.343] |
0.06677 |
0.3198 |
relative_distance
| arm |
n |
mean |
95% CI |
sd |
median |
| competitive |
30 |
1.777 |
[1.323, 2.232] |
1.218 |
1.371 |
| cartel |
30 |
4.295 |
[-0.07746, 8.668] |
11.71 |
1.744 |
buyer_utility
| arm |
n |
mean |
95% CI |
sd |
median |
| competitive |
30 |
47.57 |
[45.91, 49.22] |
4.431 |
47.24 |
| cartel |
30 |
44.4 |
[42.72, 46.08] |
4.503 |
44.16 |
hhi
| arm |
n |
mean |
95% CI |
sd |
median |
| competitive |
30 |
0.1051 |
[0.1007, 0.1096] |
0.01187 |
0.1032 |
| cartel |
30 |
0.1066 |
[0.103, 0.1103] |
0.009868 |
0.1061 |
Statistical tests
Paired t-tests on per-replication differences (treatment - baseline). Effect size is Cohen's d_z.
| metric |
treatment |
mean diff |
CI |
relative |
d_z |
p |
p (Holm) |
| average_cost |
cartel |
0.007905 |
[0.006986, 0.008824] |
+19.5% |
3.21 |
5.14e-17 |
2.57e-16 |
| bid_cv |
cartel |
0.005813 |
[-0.01908, 0.0307] |
+1.9% |
0.0872 |
0.636 |
0.743 |
| relative_distance |
cartel |
2.518 |
[-1.847, 6.882] |
+141.6% |
0.215 |
0.248 |
0.743 |
| buyer_utility |
cartel |
-3.167 |
[-3.817, -2.518] |
-6.7% |
-1.82 |
7.03e-11 |
2.81e-10 |
| hhi |
cartel |
0.001494 |
[-0.001861, 0.004848] |
+1.4% |
0.166 |
0.37 |
0.743 |
Limitations
- The cartel strategy is a simple rotation; real cartels adapt to screens.
- Screens are reported as market averages, not as a per-auction detector.
- Results come from a synthetic market; agent costs, quality and reliability are drawn from the configured distributions, not measured from real agents.
- Agents follow fixed (or simple adaptive) bidding strategies; real strategic agents may respond to the mechanism differently.
- A non-significant difference is not evidence of equivalence.
- P-values are Holm-adjusted across the comparisons in this report only.
Conclusion
- In this simulated environment,
cartel produced higher average_cost than competitive (mean difference 0.007905, 95% CI [0.006986, 0.008824]).
- No difference in
bid_cv between cartel and competitive was detected at alpha=0.05 after Holm adjustment (95% CI [-0.01908, 0.0307]).
- No difference in
relative_distance between cartel and competitive was detected at alpha=0.05 after Holm adjustment (95% CI [-1.847, 6.882]).
- In this simulated environment,
cartel produced lower buyer_utility than competitive (mean difference -3.167, 95% CI [-3.817, -2.518]).
- No difference in
hhi between cartel and competitive was detected at alpha=0.05 after Holm adjustment (95% CI [-0.001861, 0.004848]).