From 1f76081c897e01a0bd0187df33d91869b7395c32 Mon Sep 17 00:00:00 2001 From: diana3135 Date: Sat, 14 Mar 2026 23:23:44 +0100 Subject: [PATCH] =?UTF-8?q?Add=20study=5F014:=20Davis=20et=20al.=20(2011)?= =?UTF-8?q?=20=E2=80=94=20Optimal=20Reserve=20Prices=20in=20Auctions?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- studies/study_014/README.md | 58 + .../human_data/auction_human_data.csv | 2401 +++++++++++++++++ .../benchmark/llm_data/claude-3-5_1.csv | 2401 +++++++++++++++++ .../benchmark/llm_data/claude-3-5_2.csv | 2401 +++++++++++++++++ .../benchmark/llm_data/claude-3-7_1.csv | 2401 +++++++++++++++++ .../benchmark/llm_data/claude-3-7_2.csv | 2401 +++++++++++++++++ .../study_014/benchmark/llm_data/gpt-4o_1.csv | 2401 +++++++++++++++++ .../study_014/benchmark/llm_data/gpt-4o_2.csv | 2401 +++++++++++++++++ studies/study_014/index.json | 13 + studies/study_014/scripts/config.py | 181 ++ studies/study_014/scripts/evaluator.py | 137 + studies/study_014/scripts/stats_lib.py | 61 + studies/study_014/scripts/study_utils.py | 149 + ...uctioneers Pick Optimal Reserve Prices.pdf | Bin 0 -> 294802 bytes ...essing LLM Fidelity in Decision-Making.pdf | Bin 0 -> 598354 bytes studies/study_014/source/ground_truth.json | 68 + .../materials/auction_instructions.json | 65 + studies/study_014/source/metadata.json | 37 + studies/study_014/source/specification.json | 53 + 19 files changed, 17629 insertions(+) create mode 100644 studies/study_014/README.md create mode 100755 studies/study_014/benchmark/human_data/auction_human_data.csv create mode 100644 studies/study_014/benchmark/llm_data/claude-3-5_1.csv create mode 100644 studies/study_014/benchmark/llm_data/claude-3-5_2.csv create mode 100644 studies/study_014/benchmark/llm_data/claude-3-7_1.csv create mode 100644 studies/study_014/benchmark/llm_data/claude-3-7_2.csv create mode 100644 studies/study_014/benchmark/llm_data/gpt-4o_1.csv create mode 100644 studies/study_014/benchmark/llm_data/gpt-4o_2.csv create mode 100644 studies/study_014/index.json create mode 100644 studies/study_014/scripts/config.py create mode 100644 studies/study_014/scripts/evaluator.py create mode 100644 studies/study_014/scripts/stats_lib.py create mode 100644 studies/study_014/scripts/study_utils.py create mode 100644 studies/study_014/source/Davis et al. - 2011 - Do Auctioneers Pick Optimal Reserve Prices.pdf create mode 100644 studies/study_014/source/Feng et al. - 2025 - Noise Adaptation and Strategy Assessing LLM Fidelity in Decision-Making.pdf create mode 100644 studies/study_014/source/ground_truth.json create mode 100644 studies/study_014/source/materials/auction_instructions.json create mode 100644 studies/study_014/source/metadata.json create mode 100644 studies/study_014/source/specification.json diff --git a/studies/study_014/README.md b/studies/study_014/README.md new file mode 100644 index 00000000..1f4085c4 --- /dev/null +++ b/studies/study_014/README.md @@ -0,0 +1,58 @@ +# Do Auctioneers Pick Optimal Reserve Prices? + +**Authors:** Andrew M. Davis, Elena Katok, Anthony M. Kwasnica +**Year:** 2011 + +--- + +## Description + +This study investigates how auctioneers set reserve prices in second-price sealed-bid auctions (described to sellers as English auctions). A well-established theoretical result, assuming risk neutrality of the seller, is that the optimal reserve price should not depend on the number of participating bidders (Roger B. Myerson 1981). In a set of controlled laboratory experiments, seller behavior often deviates from this theoretical benchmark. + +Specifically, this study tests the Cuberoot distribution treatment with bidder counts in {1, 4, 7, 10} under the NoInfo condition. Computerized bidders follow the weakly dominant strategy of bidding their private valuations, drawn from the Cuberoot distribution F(v) = (v/100)^(1/3) with mean 25 and support [0, 100]. The seller's personal valuation is zero, and the risk-neutral optimal reserve price is 42. + +The key finding: sellers systematically increase their reserve prices as the number of bidders grows (Pearson r = 0.42, p < .001), contrary to standard auction theory. + +LLM simulation baselines for this experiment are done and reported in [Feng et al., "Noise, Adaptation, and Strategy: Assessing LLM Fidelity in Decision-Making," EMNLP 2025](https://aclanthology.org/2025.emnlp-main.391.pdf). Baselines from GPT-4o and Claude Sonnet models are available in `benchmark/`. + +## Participants + +- **N:** 40 +- **Population:** University students + +## Replicated tests (human data) + +Due to the unavailability of the original human experiment data (Davis et al. 2011), we use the replicated experiment data (Davis et al. 2023) instead. + +- **Pearson correlation (reserve price vs. number of bidders)** + Reported: r = 0.42, p < .001 + Significance level: 0.05 + +## Effect sizes & auxiliary statistics + +- F1: Mean reserve prices by number of bidders (Cuberoot distribution, NoInfo): + 1 bidder: 14.85 (SD = 19.15, n = 716), + 4 bidders: 24.30 (SD = 17.90, n = 566), + 7 bidders: 32.93 (SD = 21.25, n = 458), + 10 bidders: 39.50 (SD = 25.12, n = 660). + Overall: mean = 27.31, SD = 23.23, sell-through rate = 0.74, mean profit = 32.83. + Risk-neutral optimal reserve price = 42. + Raw data present in `ground_truth.json`. + +## Files + +**source/** +- ground_truth.json +- materials/auction_instructions.json +- metadata.json +- specification.json + +**scripts/** +- config.py +- evaluator.py +- stats_lib.py +- study_utils.py + +**benchmark/** +- human_data/auction_human_data.csv +- llm_data diff --git a/studies/study_014/benchmark/human_data/auction_human_data.csv b/studies/study_014/benchmark/human_data/auction_human_data.csv new file mode 100755 index 00000000..35027fa9 --- /dev/null +++ b/studies/study_014/benchmark/human_data/auction_human_data.csv @@ -0,0 +1,2401 @@ +Stepgroup Label,Stepgroup Loop,Group,Bidder Group,auctionPrice,highBid,myProfit,newBids,numBidders,rPrice,secondBid +rprice,1,,S.1,0,9,0,a:1:{i:0;d:9;},1,10,0 +rprice,2,,S.1,5,49,5,a:1:{i:0;d:49;},1,5,0 +rprice,3,,S.1,36,44,36,a:10:{i:0;d:44;i:1;d:36;i:2;d:10;i:3;d:7;i:4;d:7;i:5;d:6;i:6;d:5;i:7;d:4;i:8;d:3;i:9;d:0;},10,25,36 +rprice,4,,S.1,83,100,83,a:10:{i:0;d:100;i:1;d:83;i:2;d:36;i:3;d:20;i:4;d:11;i:5;d:6;i:6;d:5;i:7;d:1;i:8;d:0;i:9;d:0;},10,30,83 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+rprice,8,,S.11,64,86,64,a:10:{i:0;d:86;i:1;d:64;i:2;d:59;i:3;d:11;i:4;d:5;i:5;d:4;i:6;d:2;i:7;d:1;i:8;d:1;i:9;d:0;},10,10,64 +rprice,9,,S.11,49,97,49,a:7:{i:0;d:97;i:1;d:49;i:2;d:29;i:3;d:27;i:4;d:9;i:5;d:4;i:6;d:4;},7,20,49 +rprice,10,,S.11,49,97,49,a:7:{i:0;d:97;i:1;d:49;i:2;d:29;i:3;d:27;i:4;d:9;i:5;d:4;i:6;d:4;},7,15,49 +rprice,11,,S.11,1,9,1,a:1:{i:0;d:9;},1,1,0 +rprice,12,,S.11,33,41,33,a:4:{i:0;d:41;i:1;d:33;i:2;d:23;i:3;d:0;},4,8,33 +rprice,13,,S.11,20,83,20,a:4:{i:0;d:83;i:1;d:18;i:2;d:1;i:3;d:0;},4,20,18 +rprice,14,,S.11,64,83,64,a:7:{i:0;d:83;i:1;d:64;i:2;d:64;i:3;d:53;i:4;d:31;i:5;d:10;i:6;d:7;},7,15,64 +rprice,15,,S.11,22,75,22,a:4:{i:0;d:75;i:1;d:22;i:2;d:0;i:3;d:0;},4,8,22 +rprice,16,,S.11,5,88,5,a:1:{i:0;d:88;},1,5,0 +rprice,17,,S.11,80,83,80,a:10:{i:0;d:83;i:1;d:80;i:2;d:70;i:3;d:70;i:4;d:57;i:5;d:19;i:6;d:19;i:7;d:3;i:8;d:0;i:9;d:0;},10,10,80 +rprice,18,,S.11,0,4,0,a:1:{i:0;d:4;},1,100,0 +rprice,19,,S.11,24,70,24,a:4:{i:0;d:70;i:1;d:24;i:2;d:19;i:3;d:0;},4,8,24 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+rprice,60,,S.27,70,78,70,a:7:{i:0;d:78;i:1;d:42;i:2;d:39;i:3;d:30;i:4;d:9;i:5;d:5;i:6;d:1;},7,70,42 +rprice,1,,S.28,37,53,37,a:7:{i:0;d:53;i:1;d:37;i:2;d:27;i:3;d:24;i:4;d:14;i:5;d:9;i:6;d:1;},7,20,37 +rprice,2,,S.28,80,83,80,a:4:{i:0;d:83;i:1;d:80;i:2;d:61;i:3;d:55;},4,20,80 +rprice,3,,S.28,20,91,20,a:1:{i:0;d:91;},1,20,0 +rprice,4,,S.28,39,42,39,a:4:{i:0;d:42;i:1;d:39;i:2;d:30;i:3;d:9;},4,15,39 +rprice,5,,S.28,55,100,55,a:4:{i:0;d:100;i:1;d:55;i:2;d:2;i:3;d:0;},4,15,55 +rprice,6,,S.28,64,83,64,a:10:{i:0;d:83;i:1;d:64;i:2;d:55;i:3;d:51;i:4;d:37;i:5;d:16;i:6;d:3;i:7;d:1;i:8;d:0;i:9;d:0;},10,15,64 +rprice,7,,S.28,0,2,0,a:4:{i:0;d:2;i:1;d:1;i:2;d:0;i:3;d:0;},4,15,1 +rprice,8,,S.28,0,14,0,a:1:{i:0;d:14;},1,15,0 +rprice,9,,S.28,0,1,0,a:1:{i:0;d:1;},1,10,0 +rprice,10,,S.28,0,1,0,a:1:{i:0;d:1;},1,15,0 +rprice,11,,S.28,20,97,20,a:1:{i:0;d:97;},1,20,0 +rprice,12,,S.28,70,78,70,a:10:{i:0;d:78;i:1;d:70;i:2;d:66;i:3;d:36;i:4;d:13;i:5;d:8;i:6;d:3;i:7;d:1;i:8;d:1;i:9;d:0;},10,15,70 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+rprice,14,,S.36,78,86,78,a:10:{i:0;d:86;i:1;d:78;i:2;d:49;i:3;d:22;i:4;d:17;i:5;d:12;i:6;d:4;i:7;d:2;i:8;d:1;i:9;d:0;},10,6,78 +rprice,15,,S.36,73,91,73,a:7:{i:0;d:91;i:1;d:73;i:2;d:59;i:3;d:1;i:4;d:0;i:5;d:0;i:6;d:0;},7,4,73 +rprice,16,,S.36,0,1,0,a:1:{i:0;d:1;},1,0,0 +rprice,17,,S.36,51,68,51,a:10:{i:0;d:68;i:1;d:51;i:2;d:47;i:3;d:10;i:4;d:1;i:5;d:1;i:6;d:0;i:7;d:0;i:8;d:0;i:9;d:0;},10,6,51 +rprice,18,,S.36,1,9,1,a:1:{i:0;d:9;},1,1,0 +rprice,19,,S.36,49,49,49,a:7:{i:0;d:49;i:1;d:49;i:2;d:23;i:3;d:17;i:4;d:4;i:5;d:2;i:6;d:2;},7,4,49 +rprice,20,,S.36,10,66,10,a:7:{i:0;d:66;i:1;d:10;i:2;d:9;i:3;d:7;i:4;d:1;i:5;d:0;i:6;d:0;},7,4,10 +rprice,21,,S.36,51,97,51,a:10:{i:0;d:97;i:1;d:51;i:2;d:42;i:3;d:34;i:4;d:26;i:5;d:18;i:6;d:16;i:7;d:15;i:8;d:10;i:9;d:6;},10,6,51 +rprice,22,,S.36,0,1,0,a:1:{i:0;d:1;},1,1,0 +rprice,23,,S.36,7,33,7,a:7:{i:0;d:33;i:1;d:7;i:2;d:5;i:3;d:5;i:4;d:2;i:5;d:0;i:6;d:0;},7,4,7 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+rprice,20,,S.37,70,78,70,a:10:{i:0;d:78;i:1;d:70;i:2;d:66;i:3;d:36;i:4;d:13;i:5;d:8;i:6;d:3;i:7;d:1;i:8;d:1;i:9;d:0;},10,20,70 +rprice,21,,S.37,2,47,2,a:1:{i:0;d:47;},1,2,0 +rprice,22,,S.37,1,91,1,a:1:{i:0;d:91;},1,1,0 +rprice,23,,S.37,83,100,83,a:7:{i:0;d:100;i:1;d:83;i:2;d:49;i:3;d:7;i:4;d:4;i:5;d:2;i:6;d:0;},7,8,83 +rprice,24,,S.37,47,64,47,a:10:{i:0;d:64;i:1;d:47;i:2;d:10;i:3;d:5;i:4;d:5;i:5;d:2;i:6;d:2;i:7;d:0;i:8;d:0;i:9;d:0;},10,15,47 +rprice,25,,S.37,1,6,1,a:1:{i:0;d:6;},1,1,0 +rprice,26,,S.37,64,88,64,a:10:{i:0;d:88;i:1;d:64;i:2;d:61;i:3;d:33;i:4;d:26;i:5;d:10;i:6;d:8;i:7;d:2;i:8;d:0;i:9;d:0;},10,15,64 +rprice,27,,S.37,5,31,5,a:4:{i:0;d:31;i:1;d:1;i:2;d:0;i:3;d:0;},4,5,1 +rprice,28,,S.37,70,78,70,a:10:{i:0;d:78;i:1;d:70;i:2;d:61;i:3;d:59;i:4;d:57;i:5;d:39;i:6;d:23;i:7;d:13;i:8;d:5;i:9;d:1;},10,10,70 +rprice,29,,S.37,1,5,1,a:1:{i:0;d:5;},1,1,0 +rprice,30,,S.37,0,1,0,a:1:{i:0;d:1;},1,1,0 +rprice,31,,S.37,36,47,36,a:4:{i:0;d:47;i:1;d:36;i:2;d:5;i:3;d:0;},4,3,36 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"authors": [ + "Andrew M. Davis", + "Elena Katok", + "Anthony M. Kwasnica" + ], + "year": 2011, + "description": "This study investigates how auctioneers set reserve prices in second-price sealed-bid auctions. A well-established theoretical result, assuming risk neutrality of the seller, is that the optimal reserve price should not depend on the number of participating bidders. In a set of controlled laboratory experiments, it is found that seller behavior often deviates from the theoretical benchmarks: sellers systematically increase their reserve prices as the number of bidders grows, contrary to standard auction theory.", + "contributors": [ + { "name": "Yuanjun Feng", "github": "https://github.com/diana3135" } + ] +} diff --git a/studies/study_014/scripts/config.py b/studies/study_014/scripts/config.py new file mode 100644 index 00000000..5a38b8e8 --- /dev/null +++ b/studies/study_014/scripts/config.py @@ -0,0 +1,181 @@ +import json +import re +import numpy as np +from pathlib import Path +from typing import Dict, Any, List, Optional + +import sys +sys.path.insert(0, str(__import__("pathlib").Path(__file__).resolve().parent)) +from study_utils import BaseStudyConfig, PromptBuilder + +import random + + +class AuctionPromptBuilder(PromptBuilder): + def build_trial_prompt(self, trial_metadata): + profile = trial_metadata.get("profile", {}) + current_round = trial_metadata.get("current_round", 1) + num_bidders = trial_metadata.get("num_bidders", 1) + history = trial_metadata.get("history", []) + instructions_text = trial_metadata.get("instructions_text", "") + + full_prompt = [] + + full_prompt.append(f"You are an undergraduate student at the University of Michigan.") + full_prompt.append(f"You are {profile.get('age', 20)}, {profile.get('gender', 'Male')}, " + f"{profile.get('race', '')}, and studying {profile.get('program', '')}.\n") + + full_prompt.append("You are about to participate in an auction experiment.\n") + full_prompt.append(f"Here are the experiment instructions:\n{instructions_text}\n") + + full_prompt.append("IMPORTANT:") + full_prompt.append("- Try to maximize your total profit over 60 rounds.") + full_prompt.append("- You can only respond with an integer between 0 and 100 representing the reservation price.") + full_prompt.append("- Do not provide any explanation or additional text in your response.\n") + + # Last round result + if history: + last = history[-1] + bid_prices = last.get("bid_prices", []) + reserve = last.get("reserve_price", 0) + filtered_bids = sorted([b for b in bid_prices if b >= reserve], reverse=True) + + full_prompt.append(f"Here is your last round result:") + full_prompt.append(f"Round {last['round']}:") + full_prompt.append(f" Your Reserve Price: {reserve}") + full_prompt.append(f" Profit: {last['profit']}") + full_prompt.append(f" Number of Bidders: {last['num_bidders']}") + full_prompt.append(f" Winning Price: {last['profit']}") + if filtered_bids: + bids_str = "; ".join([f"Bidder: {i+1}, Drop-Out Price: {p}" for i, p in enumerate(filtered_bids)]) + else: + bids_str = "No bids were above your reserve price." + full_prompt.append(f" Bids higher than your reserve price: {bids_str}\n") + else: + full_prompt.append("Here is your last round result:\nNo previous round result.\n") + + # Cumulative history + if history: + full_prompt.append("Here is the history of all previous rounds:") + for h in history: + drop_out = [p if p != 0 else None for p in h["bid_prices"]] + full_prompt.append( + f"Round {h['round']}: " + f"Your Reserve Price={h['reserve_price']}, " + f"Your Profit={h['profit']}, " + f"Number of Bidders={h['num_bidders']}, " + f"Drop-Out Prices={drop_out}" + ) + full_prompt.append("") + else: + full_prompt.append("Here is the history of all previous rounds:\nNo prior history.\n") + + full_prompt.append(f"Now it's round {current_round}.") + full_prompt.append(f"Number of Bidders in this round: {num_bidders}\n") + full_prompt.append("What reserve price do you set for *this round*?") + + full_prompt.append("\nRESPONSE_SPEC (MANDATORY FORMAT):") + full_prompt.append("- Output ONLY a single integer between 0 and 100.") + full_prompt.append("- Expected lines: 1") + + return "\n".join(full_prompt) + + +class StudyDavisEtAl2011Config(BaseStudyConfig): + prompt_builder_class = AuctionPromptBuilder + REQUIRES_GROUP_TRIALS = True + + def _parse_bid_prices(self, bid_string): + return [int(x) for x in re.findall(r'd:(\d+)', str(bid_string))] + + def create_trials(self, n_trials=None): + spec = self.load_specification() + materials = self.load_material("auction_instructions") + instructions_text = materials["instructions"] + + n_subjects = n_trials if n_trials is not None else spec["participants"]["n"] + + # Load human auction data for bidder group structure + benchmark_path = self.study_path / "benchmark" / "human_data" / "auction_human_data.csv" + if not benchmark_path.exists(): + raise FileNotFoundError(f"Human data not found: {benchmark_path}") + + import pandas as pd + human_data = pd.read_csv(benchmark_path) + bidder_groups = sorted(human_data["Bidder Group"].unique()) + + trials = [] + for bg in bidder_groups[:n_subjects]: + group_data = human_data[human_data["Bidder Group"] == bg].reset_index(drop=True) + + rounds = [] + for i, row in group_data.iterrows(): + rounds.append({ + "round": i + 1, + "num_bidders": int(row["numBidders"]), + "bid_prices": self._parse_bid_prices(row["newBids"]) + }) + + profile = { + "age": random.randint(18, 22), + "gender": random.choice(["Male", "Female"]), + "race": random.choice(["White", "Asian", "Black", "Hispanic"]), + "program": random.choice(["Economics", "Psychology", "Engineering", "Business"]) + } + + trials.append({ + "sub_study_id": "second_price_auction", + "bidder_group": bg, + "rounds": rounds, + "profile": profile, + "instructions_text": instructions_text + }) + + return trials + + def aggregate_results(self, raw_results): + aggregated = {"by_bidder_count": {}, "all_observations": []} + + for record in raw_results.get("individual_data", []): + response_text = record.get("response_text", "") + trial_info = record.get("trial_info", {}) + num_bidders = trial_info.get("num_bidders") + + match = re.search(r"(\d+)", str(response_text)) + if not match: + continue + reserve_price = int(match.group(1)) + if reserve_price < 0 or reserve_price > 100: + continue + + aggregated["all_observations"].append({ + "reserve_price": reserve_price, + "num_bidders": num_bidders + }) + + key = str(num_bidders) + if key not in aggregated["by_bidder_count"]: + aggregated["by_bidder_count"][key] = [] + aggregated["by_bidder_count"][key].append(reserve_price) + + # Compute summary statistics + final = {"descriptive_statistics": {}, "inferential_statistics": []} + + for bc, prices in aggregated["by_bidder_count"].items(): + final["descriptive_statistics"][f"mean_rPrice_{bc}_bidders"] = float(np.mean(prices)) + final["descriptive_statistics"][f"sd_rPrice_{bc}_bidders"] = float(np.std(prices)) + final["descriptive_statistics"][f"n_{bc}_bidders"] = len(prices) + + all_obs = aggregated["all_observations"] + if len(all_obs) >= 10: + rprices = np.array([o["reserve_price"] for o in all_obs]) + nbidders = np.array([o["num_bidders"] for o in all_obs]) + r = np.corrcoef(rprices, nbidders)[0, 1] + final["inferential_statistics"].append({ + "test": "pearson_correlation", + "variables": ["reserve_price", "num_bidders"], + "statistic": float(r), + "n": len(all_obs) + }) + + return final diff --git a/studies/study_014/scripts/evaluator.py b/studies/study_014/scripts/evaluator.py new file mode 100644 index 00000000..6bf93b54 --- /dev/null +++ b/studies/study_014/scripts/evaluator.py @@ -0,0 +1,137 @@ +import json +import re +import numpy as np +from pathlib import Path +from typing import Dict, Any + +import sys +sys.path.insert(0, str(__import__("pathlib").Path(__file__).resolve().parent)) +from stats_lib import parse_p_value_from_reported + +_ground_truth_cache = None + + +def _expected_direction_to_int(expected_dir_str: str) -> int: + if not expected_dir_str: + return 0 + s = str(expected_dir_str).lower() + if s in ("positive", "greater", ">"): + return 1 + if s in ("negative", "less", "<"): + return -1 + return 0 + + +def evaluate_study(results): + """ + Evaluates the agent's performance on the Davis et al. (2011) auction study. + Tests whether the agent exhibits a positive correlation between reserve price + and number of bidders (F1). + """ + global _ground_truth_cache + + if _ground_truth_cache is None: + study_dir = Path(__file__).resolve().parent.parent / "source" + with open(study_dir / "ground_truth.json", "r") as f: + _ground_truth_cache = json.load(f) + + ground_truth = _ground_truth_cache + sig_level = 0.05 + + # Extract agent reserve prices and bidder counts + reserve_prices = [] + bidder_counts = [] + by_bidder_count = {} + + for participant in results.get("individual_data", []): + for response in participant.get("responses", []): + response_text = response.get("response_text", "") + trial_info = response.get("trial_info", {}) + num_bidders = trial_info.get("num_bidders") + + if num_bidders is None: + continue + + match = re.search(r"(\d+)", str(response_text)) + if not match: + continue + rp = int(match.group(1)) + if rp < 0 or rp > 100: + continue + + reserve_prices.append(rp) + bidder_counts.append(num_bidders) + + key = str(num_bidders) + if key not in by_bidder_count: + by_bidder_count[key] = [] + by_bidder_count[key].append(rp) + + # Get ground truth for F1 + test_results = [] + study_gt = ground_truth["studies"][0] + finding = study_gt["findings"][0] + finding_id = finding["finding_id"] + stat_test = finding["statistical_tests"][0] + expected_dir = _expected_direction_to_int(stat_test.get("expected_direction", "positive")) + reported_stats = stat_test.get("reported_statistics", "") + + human_p_value = None + human_significant = None + parsed_p, parsed_sig, _ = parse_p_value_from_reported(reported_stats, sig_level) + if parsed_p is not None: + human_p_value = parsed_p + human_significant = parsed_sig + + human_r = ground_truth["studies"][0]["findings"][0]["original_data_points"]["data"]["overall"]["pearson_r"] + + # Compute agent statistics + agent_r = None + p_value = None + agent_significant = None + direction_match = None + mean_by_bidders = {} + + for bc, prices in by_bidder_count.items(): + mean_by_bidders[bc] = float(np.mean(prices)) + + if len(reserve_prices) >= 10: + rp_arr = np.array(reserve_prices, dtype=float) + bc_arr = np.array(bidder_counts, dtype=float) + agent_r = float(np.corrcoef(rp_arr, bc_arr)[0, 1]) + + if not np.isnan(agent_r): + # Approximate p-value from r and n using t-distribution + n = len(reserve_prices) + t_stat = agent_r * np.sqrt((n - 2) / (1 - agent_r ** 2)) + # Two-tailed p-value approximation (normal for large n) + from math import erfc, sqrt + p_value = erfc(abs(t_stat) / sqrt(2)) + + agent_significant = p_value < sig_level + agent_dir = 1 if agent_r > 0 else -1 + direction_match = (expected_dir == 0) or (agent_dir == expected_dir) + + replication = None + if human_significant is not None and agent_significant is not None and direction_match is not None: + replication = human_significant and agent_significant and direction_match + + test_results.append({ + "study_id": "second_price_auction", + "sub_study_id": "second_price_auction", + "finding_id": finding_id, + "scenario": "reserve_price_bidder_correlation", + "n_agent_observations": len(reserve_prices), + "mean_agent_by_bidders": mean_by_bidders, + "agent_pearson_r": agent_r, + "t_stat": float(t_stat) if agent_r is not None and not np.isnan(agent_r) else None, + "p_value": float(p_value) if p_value is not None else None, + "significant": agent_significant, + "direction_match": direction_match, + "human_pearson_r": human_r, + "human_p_value": human_p_value, + "human_significant": human_significant, + "replication": replication, + }) + + return {"test_results": test_results} diff --git a/studies/study_014/scripts/stats_lib.py b/studies/study_014/scripts/stats_lib.py new file mode 100644 index 00000000..1e0dc0aa --- /dev/null +++ b/studies/study_014/scripts/stats_lib.py @@ -0,0 +1,61 @@ +""" +Parse p-value from reported_statistics strings. +""" + +import re +from typing import Tuple, Optional + + +def parse_p_value_from_reported( + reported_statistics: str, significance_level: float = 0.05 +) -> Tuple[Optional[float], bool, str]: + """ + Parse p-value from reported_statistics string. + + Handles formats like: + - "p < .001" or "p < 0.001" + - "p < .05" or "p < 0.05" + - "p = 0.023" + - "r = 0.42, p < .001" + + Returns: + tuple: (p_value, is_significant, confidence) + """ + if significance_level is None: + significance_level = 0.05 + + if not reported_statistics: + return None, False, "low" + + text = reported_statistics.lower() + + exact_match = re.search(r"p\s*[=:]\s*([0-9.]+)", text) + if exact_match: + p_val = float(exact_match.group(1)) + is_sig = p_val <= significance_level if significance_level is not None else False + return p_val, is_sig, "high" + + inequality_match = re.search(r"p\s*[<>]\s*([0-9.]+)", text) + if inequality_match: + threshold = float(inequality_match.group(1)) + is_less_than = "<" in text[ + inequality_match.start() : inequality_match.end() + ] + + if is_less_than: + p_val = threshold / 2.0 + is_sig = True + return p_val, is_sig, "medium" + else: + p_val = threshold + is_sig = threshold < significance_level if significance_level is not None else False + return p_val, is_sig, "medium" + + r_match = re.search(r"r\s*=\s*([-0-9.]+)", text) + if r_match: + r_val = abs(float(r_match.group(1))) + if r_val > 0.3: + return 0.025, True, "low" + return 0.10, False, "low" + + return None, False, "low" diff --git a/studies/study_014/scripts/study_utils.py b/studies/study_014/scripts/study_utils.py new file mode 100644 index 00000000..aa58ed65 --- /dev/null +++ b/studies/study_014/scripts/study_utils.py @@ -0,0 +1,149 @@ +""" +Standalone study utilities: BaseStudyConfig and PromptBuilder. +""" +import json +import re +from abc import ABC, abstractmethod +from pathlib import Path +from typing import Dict, Any, List, Optional + + +class PromptBuilder: + """Build prompts from study specification and materials. study_path = source directory.""" + + def __init__(self, study_path: Path): + self.study_path = Path(study_path) + self.materials_path = self.study_path / "materials" + with open(self.study_path / "specification.json", "r", encoding="utf-8", errors="replace") as f: + self.specification = json.load(f) + instructions_file = self.materials_path / "instructions.txt" + self.instructions = instructions_file.read_text(encoding="utf-8", errors="replace") if instructions_file.exists() else None + system_prompt_file = self.materials_path / "system_prompt.txt" + self.system_prompt_template = system_prompt_file.read_text(encoding="utf-8", errors="replace") if system_prompt_file.exists() else None + + def build_system_prompt(self, participant_profile: Dict[str, Any] = None) -> Optional[str]: + return self.system_prompt_template + + def get_system_prompt_template(self) -> Optional[str]: + return self.system_prompt_template + + def build_trial_prompt(self, trial_data: Dict[str, Any]) -> str: + return self._build_generic_trial_prompt(trial_data) + + def get_instructions(self) -> str: + return self.instructions if self.instructions else "No instructions provided." + + def _fill_template(self, template: str, data: Dict[str, Any]) -> str: + result = template + nested_pattern = r"\{\{([\w.]+)\}\}" + def replace_nested(match): + path = match.group(1) + value = data + for part in path.split("."): + if isinstance(value, dict) and part in value: + value = value[part] + else: + return match.group(0) + return str(value) + result = re.sub(nested_pattern, replace_nested, result) + if_pattern = r"\{\{#if\s+(\w+)\}\}(.*?)\{\{/if\}\}" + def replace_if(match): + if match.group(1) in data and data[match.group(1)]: + return match.group(2) + return "" + result = re.sub(if_pattern, replace_if, result, flags=re.DOTALL) + each_pattern = r"\{\{#each\s+(\w+)\}\}(.*?)\{\{/each\}\}" + def replace_each(match): + var_name, content = match.group(1), match.group(2) + if var_name not in data: + return "" + items = data[var_name] + if isinstance(items, dict): + parts = [content.replace("{{@key}}", str(k)).replace("{{this}}", str(v)) for k, v in items.items()] + return "\n".join(parts) + if isinstance(items, list): + parts = [content.replace("{{@index}}", str(i + 1)).replace("{{this}}", str(item)) for i, item in enumerate(items)] + return "\n".join(parts) + return "" + result = re.sub(each_pattern, replace_each, result, flags=re.DOTALL) + result = re.sub(r"\{\{[^}]+\}\}", "", result) + return result + + def _build_generic_trial_prompt(self, trial_data: Dict[str, Any]) -> str: + return f"Trial {trial_data.get('trial_number', '?')}: Please respond to the following stimulus." + + +class BaseStudyConfig(ABC): + """Study config base. study_path = study root (e.g. studies/study_001); data under source/.""" + + prompt_builder_class = PromptBuilder + + def __init__(self, study_path: Path, specification: Dict[str, Any]): + self.study_path = Path(study_path) + self.source_path = self.study_path / "source" + self.specification = specification + self.study_id = specification["study_id"] + self.prompt_builder = self.prompt_builder_class(self.source_path) + + def load_material(self, sub_study_id: str) -> Dict[str, Any]: + file_path = self.source_path / "materials" / f"{sub_study_id}.json" + if not file_path.exists(): + raise FileNotFoundError(f"Material not found: {file_path}") + with open(file_path, "r", encoding="utf-8") as f: + return json.load(f) + + def load_metadata(self) -> Dict[str, Any]: + with open(self.source_path / "metadata.json", "r", encoding="utf-8") as f: + return json.load(f) + + def load_specification(self) -> Dict[str, Any]: + with open(self.source_path / "specification.json", "r", encoding="utf-8") as f: + return json.load(f) + + def load_ground_truth(self) -> Dict[str, Any]: + with open(self.source_path / "ground_truth.json", "r", encoding="utf-8") as f: + return json.load(f) + + def extract_numeric(self, text: str, default: float = 0.0) -> float: + if text is None: + return default + match = re.search(r"(-?\d+\.?\d*)", str(text)) + return float(match.group(1)) if match else default + + def extract_choice(self, text: str, options: List[str] = None) -> Optional[int]: + if text is None: + return None + text_s = str(text).strip() + if options: + for i, opt in enumerate(options): + if opt.lower() in text_s.lower(): + return i + match = re.search(r"\b([A-Z])\b", text_s.upper()) + if match: + return ord(match.group(1)) - ord("A") + return None + + @abstractmethod + def create_trials(self, n_trials: Optional[int] = None) -> List[Dict[str, Any]]: + raise NotImplementedError + + def get_prompt_builder(self) -> PromptBuilder: + return self.prompt_builder + + def get_instructions(self) -> str: + return self.prompt_builder.get_instructions() + + def aggregate_results(self, raw_results: Dict[str, Any]) -> Dict[str, Any]: + return raw_results + + def custom_scoring(self, results: Dict[str, Any], ground_truth: Dict[str, Any]) -> Optional[Dict[str, float]]: + return None + + def get_n_participants(self) -> int: + return self.specification["participants"]["n"] + + def get_study_type(self) -> str: + return self.specification.get("study_type", self.study_id) + + def __repr__(self) -> str: + return f"{self.__class__.__name__}(study_id='{self.study_id}')" diff --git a/studies/study_014/source/Davis et al. - 2011 - Do Auctioneers Pick Optimal Reserve Prices.pdf b/studies/study_014/source/Davis et al. - 2011 - Do Auctioneers Pick Optimal Reserve Prices.pdf new file mode 100644 index 0000000000000000000000000000000000000000..066e1230af05d03933496cc0d84173acd6780bb7 GIT binary patch literal 294802 zcmeFa1yoks-Zc&qB1m_4NIi6ShjgPf4_(4Tm$bBWw{$2i-60Lq9nvk`AD-iVujgLx zd-?yz`NlUK=Qtd&-FxldnrrSkSMIeXmlqMEW29$+C0||{{0z&?M#Mm5t#1a)!vj#V z*9SS<00Cmwww3@fQwtE#79eJ!2Lg%!4Xh1;0OfBN)#dcffCeCdj2_6=)QRW?iaY*};+ey?sd!-~X1DegcUeEFJmrJ}l76 z@cWJTN8bowWVw(3>oUQ}%Kift=wYP@-V9jKXM7#(W|=2mv^lP_NzcBMGe@_qmznUKSwFe{*>zzHQQ^NdfyZ>QKJg5Qs 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Davis", + "Elena Katok", + "Anthony M. Kwasnica" + ], + "year": 2011, + "studies": [ + { + "study_id": "second_price_auction", + "study_name": "Second-price sealed-bid auction with Cuberoot distribution and variable bidder counts", + "findings": [ + { + "finding_id": "F1", + "main_hypothesis": "The optimal reserve price should not depend on the number of participating bidders (under risk neutrality). However, sellers systematically increase reserve prices as the number of bidders grows.", + "statistical_tests": [ + { + "test_name": "Random-effects regression", + "statistical_hypothesis": "Positive coefficient on number of bidders in a regression of reserve price on bidder count", + "reported_statistics": "coefficient on n = 2.98, p < .001 (original); Pearson r = 0.42, p < .001", + "significance_level": 0.05, + "expected_direction": "positive" + } + ], + "original_data_points": { + "description": "Mean reserve prices by number of bidders. Original experiment at Penn State (Davis et al. 2011), replicated at University of Michigan (Davis et al. 2023). Data below from UMich replication, Cuberoot distribution, n in {1,4,7,10}, NoInfo condition.", + "data": { + "overall": { + "mean_reserve_price": 27.31, + "sd_reserve_price": 23.23, + "n_subjects": 40, + "n_rounds": 60, + "n_observations": 2400, + "sell_through_rate": 0.74, + "mean_profit": 32.83, + "entropy": 5.08, + "pearson_r": 0.42, + "optimal_reserve_price_risk_neutral": 42 + }, + "1_bidder": { + "mean_reserve_price": 14.85, + "sd_reserve_price": 19.15, + "n_observations": 716 + }, + "4_bidders": { + "mean_reserve_price": 24.30, + "sd_reserve_price": 17.90, + "n_observations": 566 + }, + "7_bidders": { + "mean_reserve_price": 32.93, + "sd_reserve_price": 21.25, + "n_observations": 458 + }, + "10_bidders": { + "mean_reserve_price": 39.50, + "sd_reserve_price": 25.12, + "n_observations": 660 + } + } + } + } + ] + } + ] +} diff --git a/studies/study_014/source/materials/auction_instructions.json b/studies/study_014/source/materials/auction_instructions.json new file mode 100644 index 00000000..089f620e --- /dev/null +++ b/studies/study_014/source/materials/auction_instructions.json @@ -0,0 +1,65 @@ +{ + "sub_study_id": "second_price_auction", + "instructions": "You are a seller of a fictitious product. To make money, you must sell that product in an auction. In each auction, you will be selling your product to a different number of computerized buyers. To sell the product, you enter the minimum value that you are willing to sell this product for; this amount is your Reservation Price.\n\nBefore entering your Reservation Price, you will know the number of computerized buyers participating in your auction for each round. Each of these buyers will have a maximum willingness to pay for your product. The maximum willingness to pay is an integer between 0 and 100.\n\nIn each auction, bids ascend until all buyers reach their maximum willingness to pay. Some buyers will be forced to stop bidding as their limits are reached. The auction ends when one buyer remains. The amount where each buyer stops bidding in the auction is called the Drop-Out Price.\n\nThe buyer with the highest Drop-Out Price wins so long as that amount is equal to or above your Reservation Price. If all of the Drop-Out Prices are below your Reservation Price, your product will not be sold, and you will earn zero in that round. The profit calculation is as follows:\n\nYour Profit = Second Highest Drop-Out Price if the second highest Drop-Out Price is equal to or above your Reservation Price.\nYour Profit = Reservation Price if the highest Drop-Out Price is above the Reservation Price, but the second highest Drop-Out Price is below the Reservation Price.\nYour Profit = 0 if all the Drop-Out Prices are below the Reservation Price.\nEach auction round, you will have one unit of the product to sell, regardless of whether or not you sold it in the previous round. You will participate in 60 consecutive auctions.\n\nFor each round, the number of buyers is randomly drawn as 1, 4, 7, or 10, each number being equally likely. The maximum amount a buyer is willing to pay is a whole number from 0 to 100.", + "items": [ + { + "id": "auction_round", + "type": "sequential_decision", + "description": "Seller sets a reserve price each round in a second-price sealed-bid auction (described as English auction) with computerized bidders.", + "response_format": "integer 0-100", + "metadata": { + "n_rounds": 60, + "bidder_counts": [1, 4, 7, 10], + "value_distribution": { + "name": "Cuberoot", + "cdf": "F(v) = (v/100)^(1/3)", + "mean": 25, + "sd": 28.4, + "support": [0, 100] + }, + "seller_personal_valuation": 0, + "optimal_reserve_risk_neutral": 42, + "profit_rules": { + "case_1": "Second highest drop-out price, if second highest drop-out price >= reserve price", + "case_2": "Reserve price, if highest drop-out price >= reserve but second highest < reserve", + "case_3": "0, if all drop-out prices < reserve price" + }, + "examples": [ + { + "reserve": 60, + "second_highest": 75, + "profit": 75 + }, + { + "reserve": 40, + "second_highest": 30, + "highest": 60, + "profit": 40 + }, + { + "reserve": 60, + "highest": 55, + "profit": 0 + } + ], + "sample_dropout_prices": [ + [4, 32, 0, 16, 67, 47, 0, 12, 0, 0], + [1, 5, 39, 0, 21, 81, 5, 0, 7, 1], + [2, 1, 1, 7, 3, 4, 1, 84, 8, 58], + [2, 0, 62, 2, 1, 0, 68, 20, 92, 8], + [5, 0, 4, 0, 16, 43, 1, 50, 2, 0], + [43, 7, 39, 7, 6, 0, 23, 25, 14, 12], + [71, 0, 17, 44, 15, 15, 3, 0, 84, 54], + [1, 91, 11, 60, 1, 36, 91, 30, 3, 0], + [1, 1, 0, 15, 0, 57, 3, 9, 93, 5], + [10, 2, 18, 71, 0, 12, 79, 64, 19, 10] + ], + "distribution_summary": { + "average": 25, + "min": 0, + "max": 100 + } + } + } + ] +} diff --git a/studies/study_014/source/metadata.json b/studies/study_014/source/metadata.json new file mode 100644 index 00000000..6ca3edf3 --- /dev/null +++ b/studies/study_014/source/metadata.json @@ -0,0 +1,37 @@ +{ + "id": "study_014", + "title": "Do Auctioneers Pick Optimal Reserve Prices?", + "authors": [ + "Andrew M. Davis", + "Elena Katok", + "Anthony M. Kwasnica" + ], + "year": 2011, + "domain": "behavioral_economics", + "subdomain": "auction_theory", + "keywords": [ + "reserve_prices", + "second_price_auction", + "behavioral_operations", + "bounded_rationality", + "bidder_count" + ], + "difficulty": "hard", + "description": "This study investigates how auctioneers set reserve prices in second-price sealed-bid auctions. A well-established theoretical result, assuming risk neutrality of the seller, is that the optimal reserve price should not depend on the number of participating bidders. In a set of controlled laboratory experiments, it is found that seller behavior often deviates from the theoretical benchmarks: sellers systematically increase their reserve prices as the number of bidders grows, contrary to standard auction theory.", + "scenarios": [ + "second_price_auction" + ], + "findings": [ + { + "finding_id": "F1", + "main_hypothesis": "Sellers increase reserve prices with the number of bidders, contrary to the theoretical prediction that optimal reserve price is independent of bidder count.", + "weight": 1.0, + "tests": [ + { + "test_name": "Pearson correlation", + "weight": 1.0 + } + ] + } + ] +} diff --git a/studies/study_014/source/specification.json b/studies/study_014/source/specification.json new file mode 100644 index 00000000..34251bab --- /dev/null +++ b/studies/study_014/source/specification.json @@ -0,0 +1,53 @@ +{ + "study_id": "davis_et_al_2011_reserve_prices", + "title": "Do Auctioneers Pick Optimal Reserve Prices?", + "participants": { + "n": 40, + "population": "University students", + "recruitment_source": null, + "demographics": { + "profile_fields": ["age", "gender", "race", "program"] + } + }, + "design": { + "type": "Within-subjects", + "factors": [ + { + "name": "Number of Bidders", + "levels": [1, 4, 7, 10], + "type": "Within-Subjects" + }, + { + "name": "Round", + "levels": "1-60", + "type": "Within-Subjects" + } + ], + "mechanism": "Second-price sealed-bid auction (described as English auction)", + "bidder_type": "Computerized bidders following weakly dominant strategy (bid equal to valuation)", + "value_distribution": { + "name": "Cuberoot", + "cdf": "F(v) = (v/100)^(1/3)", + "support": [0, 100], + "mean": 25, + "sd": 28.4 + }, + "seller_personal_valuation": 0, + "optimal_reserve_price_risk_neutral": 42, + "reserve_price_range": [0, 100], + "n_rounds": 60, + "information_condition": "NoInfo" + }, + "procedure": { + "steps": [ + "Seller receives complete auction instructions including rules, profit calculation examples, and a table and histogram of the drop-out price distribution.", + "Seller is assigned a demographic profile (age, gender, race, academic program).", + "Each round, seller observes the number of computerized bidders (randomly drawn from 1, 4, 7, or 10, equally likely).", + "Seller sets a reserve price (integer 0-100).", + "Computerized bidders bid up to their private valuations (drawn from the Cuberoot distribution). Bidders with valuations below the reserve price do not participate.", + "Seller receives feedback: drop-out prices for bidders above the reserve, whether some bidders were below the reserve, the winning bid, and profit for the round.", + "Seller sees cumulative history of all previous rounds before making the next decision.", + "Process repeats for 60 consecutive rounds." + ] + } +}

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