From b00de087f8e931d3aa6e109b9f14a65227f4b53a Mon Sep 17 00:00:00 2001
From: Maxime MORGE <maxime.morge@univ-lille.fr>
Date: Wed, 26 Mar 2025 14:04:26 +0100
Subject: [PATCH] Investment game results
---
README.md | 82 ++--
data/investment/investment.csv | 140 +++++-
data/investment/investment.old.csv | 97 -----
figures/investment/investment.svg | 527 +++++++++++++++--------
src/investment/investment.py | 56 ++-
src/investment/investment_draw.py | 2 +-
src/investment/investment_experiments.py | 6 +-
7 files changed, 532 insertions(+), 378 deletions(-)
delete mode 100644 data/investment/investment.old.csv
diff --git a/README.md b/README.md
index e6bb90c..6205016 100644
--- a/README.md
+++ b/README.md
@@ -15,47 +15,55 @@ directions to overcome the current limitations of LLMs.
## Consistency
-To assess the decision-making consistency of various LLMs, we introduce an
-investment game that allows us to observe whether LLMs follow stable
-decision-making patterns or react erratically to variations in the game’s
-parameters.
-
-An investor must allocate a basket (p_t^A, p_t^B) of 100 points between Asset A
-and Asset B. The value of these points depends on two random parameters (a_t,
-b_t), which determine how much money is received per allocated point.
-
-For example, if a = 0.8 and b = 0.5, this means that each point allocated to
-Asset A is worth $0.8, while each point allocated to Asset B yields $0.5. The
-game is played 25 times to analyze the consistency of the investor’s
-decision-making.
-
-The investor’s decisions are then evaluated using an index called the Critical
-Cost Efficiency Index (CCEI), which measures whether decisions adhere to a
-certain level of economic rationality. This index is commonly used in
-experimental economics and behavioral sciences to determine whether an
-individual’s choices comply with the Generalized Axiom of Revealed Preference
-(GARP). If an individual violates rational choice consistency, it is possible to
-make a minimal budget adjustment (reducing resources) to align their decisions
-with rationality. The CCEI quantifies the smallest budget reduction necessary to
-make the choices consistent with rational principles.
-
-Each basket’s budget is calculated as follows:
+To evaluate the decision-making consistency of various LLMs, we introduce an investment
+game designed to test whether these models follow stable decision-making patterns or
+react erratically to changes in the game’s parameters.
+
+In the game, an investor allocates a basket \((p_t^A, p_t^B)\) of 100 points between two assets:
+Asset A and Asset B. The value of these points depends on two random parameters \((a_t, b_t)\),
+which determine the monetary return per allocated point.
+
+For example, if \(a_t = 0.8\) and \(b_t = 0.5\), each point assigned to Asset A is worth $0.8,
+while each point allocated to Asset B yields $0.5. The game is played 25 times to assess
+the consistency of the investor’s decisions.
+
+To evaluate the rationality of the decisions, we use the **Critical Cost Efficiency Index (CCEI)**,
+a widely used measure in experimental economics and behavioral sciences. The CCEI assesses
+whether choices adhere to the **Generalized Axiom of Revealed Preference (GARP)**,
+a fundamental principle of rational decision-making.
+
+If an individual violates rational choice consistency,
+the CCEI determines the minimal budget adjustment required to make their
+decisions align with rationality. Mathematically, the budget for each basket is calculated as:
+
+\[
I_t = p_t^A \times a_t + p_t^B \times b_t
+\]
-The CCEI index is derived from observed decisions. It is based on a linear
-optimization problem that seeks the smallest necessary adjustment to budget
-constraints to make the decisions conform to a rational model.
+The CCEI is derived from observed decisions by solving a linear optimization
+problem that finds the largest \(\lambda\) (where \(0 \leq \lambda \leq 1\))
+such that for every observation, the adjusted decisions satisfy the rationality constraint:
+
+\[
+p^_t \cdot x_s \leq \lambda I_t
+\]
+
+This means that if we slightly reduce the budget (multiplying it by \(\lambda\)),
+the choices will become consistent with rational decision-making.
+A CCEI close to 1 indicates high rationality and consistency with economic theory.
+A low CCEEI** suggests irrational or inconsistent decision-making.
+
+To ensure response consistency, each model undergoes 30 iterations of the game
+with a fixed temperature of 0.0.
+
+The results indicate significant differences in decision-making consistency among the evaluated models.
+Mistral-Small demonstrates the highest level of rationality, with CCEI values consistently above 0.75.
+Llama 3 performs moderately well, with CCEI values ranging between 0.2 and 0.74.
+DeepSeek R1 exhibits inconsistent behavior, with CCEI scores varying widely between 0.15 and 0.83
+
+
-We aim to find the largest \lambda (0 ≤ λ ≤ 1) such that, for every observation,
-the adjusted decisions satisfy the rationality constraint: p^_t \cdot x_s \leq
-\lambda I_t This means that if we slightly reduce the individual’s budget (by
-multiplying it by \lambda), their choices will become consistent with
-rationality.
-A CCEI close to 1 indicates that the choices are rational and consistent with
-rational choice theory, whereas a low CCEI suggests irrational behavior. For
-each model, 30 iterations of the game are conducted with a fixed temperature of
-0.0 to maximize response consistency.
## Preferences
diff --git a/data/investment/investment.csv b/data/investment/investment.csv
index 43aa27b..c7d1789 100644
--- a/data/investment/investment.csv
+++ b/data/investment/investment.csv
@@ -1,21 +1,121 @@
iteration,model,temperature,ccei
-1,optimal,0.0,1.0
-2,optimal,0.0,1.0
-3,optimal,0.0,1.0
-4,optimal,0.0,1.0
-5,optimal,0.0,1.0
-6,optimal,0.0,1.0
-7,optimal,0.0,1.0
-8,optimal,0.0,1.0
-9,optimal,0.0,1.0
-10,optimal,0.0,1.0
-1,random,0.0,1.0
-2,random,0.0,1.0
-3,random,0.0,1.0
-4,random,0.0,1.0
-5,random,0.0,1.0
-6,random,0.0,1.0
-7,random,0.0,1.0
-8,random,0.0,1.0
-9,random,0.0,1.0
-10,random,0.0,1.0
+1,random,0.0,0.30081300813008127
+2,random,0.0,0.29500000000000004
+3,random,0.0,0.24739884393063583
+4,random,0.0,0.2987012987012987
+5,random,0.0,0.3548387096774194
+6,random,0.0,0.3986486486486487
+7,random,0.0,0.2810650887573965
+8,random,0.0,0.35494880546075086
+9,random,0.0,0.272
+10,random,0.0,0.22171945701357465
+11,random,0.0,0.3150105708245243
+12,random,0.0,0.25641025641025644
+13,random,0.0,0.1569506726457399
+14,random,0.0,0.247787610619469
+15,random,0.0,0.5156950672645739
+16,random,0.0,0.2645739910313901
+17,random,0.0,0.40444444444444444
+18,random,0.0,0.27455919395465994
+19,random,0.0,0.20800000000000002
+20,random,0.0,0.20930232558139536
+21,random,0.0,0.3823529411764706
+22,random,0.0,0.49244712990936557
+23,random,0.0,0.2
+24,random,0.0,0.46881287726358145
+25,random,0.0,0.30916414904330314
+26,random,0.0,0.21908602150537634
+27,random,0.0,0.21929824561403508
+28,random,0.0,0.23555555555555555
+29,random,0.0,0.4501510574018127
+30,random,0.0,0.2896174863387978
+1,llama3,0.0,0.5533333333333333
+2,llama3,0.0,0.23636363636363636
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+7,llama3,0.0,0.2
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+9,llama3,0.0,0.6133333333333333
+10,llama3,0.0,0.4314720812182741
+11,llama3,0.0,0.665
+12,llama3,0.0,0.43533930857874514
+13,llama3,0.0,0.5
+14,llama3,0.0,0.519277108433735
+15,llama3,0.0,0.27586206896551724
+16,llama3,0.0,0.5555555555555556
+17,llama3,0.0,0.5
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+19,llama3,0.0,0.4246575342465753
+20,llama3,0.0,0.25
+21,llama3,0.0,0.23809523809523808
+22,llama3,0.0,0.3333333333333333
+23,llama3,0.0,0.475
+24,llama3,0.0,0.6666666666666666
+25,llama3,0.0,0.3151079136690647
+26,llama3,0.0,0.3368421052631579
+27,llama3,0.0,0.742
+28,llama3,0.0,0.5333333333333333
+29,llama3,0.0,0.5172413793103449
+30,llama3,0.0,0.5
+1,mistral-small,0.0,1.0
+2,mistral-small,0.0,0.6222222222222222
+3,mistral-small,0.0,0.8866666666666667
+4,mistral-small,0.0,0.90625
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+11,mistral-small,0.0,0.8333333333333334
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+13,mistral-small,0.0,0.925
+14,mistral-small,0.0,0.78
+15,mistral-small,0.0,0.804
+16,mistral-small,0.0,0.75
+17,mistral-small,0.0,0.84
+18,mistral-small,0.0,0.625
+19,mistral-small,0.0,0.90625
+20,mistral-small,0.0,0.8166666666666667
+21,mistral-small,0.0,0.875
+22,mistral-small,0.0,0.9866666666666667
+23,mistral-small,0.0,0.7733333333333333
+24,mistral-small,0.0,0.92
+25,mistral-small,0.0,0.8571428571428571
+26,mistral-small,0.0,0.9375
+27,mistral-small,0.0,0.7150000000000001
+28,mistral-small,0.0,0.9625
+29,mistral-small,0.0,0.8928571428571429
+30,mistral-small,0.0,0.802
+1,deepseek-r1,0.0,0.25
+2,deepseek-r1,0.0,0.5882352941176471
+3,deepseek-r1,0.0,0.42207792207792205
+4,deepseek-r1,0.0,0.335
+5,deepseek-r1,0.0,0.22105263157894736
+6,deepseek-r1,0.0,0.22999999999999998
+7,deepseek-r1,0.0,0.3058510638297872
+8,deepseek-r1,0.0,0.32142857142857145
+9,deepseek-r1,0.0,0.6711409395973154
+10,deepseek-r1,0.0,0.25
+11,deepseek-r1,0.0,0.75
+12,deepseek-r1,0.0,0.8315217391304347
+13,deepseek-r1,0.0,0.4597701149425288
+14,deepseek-r1,0.0,0.32142857142857145
+15,deepseek-r1,0.0,0.16875
+16,deepseek-r1,0.0,0.25157232704402516
+17,deepseek-r1,0.0,0.574712643678161
+18,deepseek-r1,0.0,0.28776978417266186
+19,deepseek-r1,0.0,0.32142857142857145
+20,deepseek-r1,0.0,0.7304347826086957
+21,deepseek-r1,0.0,0.17329910141206675
+22,deepseek-r1,0.0,0.175
+23,deepseek-r1,0.0,0.45454545454545453
+24,deepseek-r1,0.0,0.2992700729927008
+25,deepseek-r1,0.0,0.34
+26,deepseek-r1,0.0,0.2
+27,deepseek-r1,0.0,0.3333333333333333
+28,deepseek-r1,0.0,0.1870967741935484
+29,deepseek-r1,0.0,0.2575
+30,deepseek-r1,0.0,0.1514285714285714
diff --git a/data/investment/investment.old.csv b/data/investment/investment.old.csv
deleted file mode 100644
index d6fb25e..0000000
--- a/data/investment/investment.old.csv
+++ /dev/null
@@ -1,97 +0,0 @@
-iteration,model,temperature,ccei
-1,random,0.0,0.1993
-2,random,0.0,0.2841
-3,random,0.0,0.2584
-4,random,0.0,0.3276
-5,random,0.0,0.3676
-6,random,0.0,0.1505
-7,random,0.0,0.1047
-8,random,0.0,0.1385
-9,random,0.0,0.1866
-10,random,0.0,0.3135
-11,random,0.0,0.1835
-12,random,0.0,0.29
-13,random,0.0,0.2523
-14,random,0.0,0.2014
-15,random,0.0,0.1676
-16,random,0.0,0.2469
-17,random,0.0,0.2429
-18,random,0.0,0.1676
-19,random,0.0,0.1818
-20,random,0.0,0.3804
-21,random,0.0,0.2718
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-23,random,0.0,0.2473
-24,random,0.0,0.1942
-25,random,0.0,0.2857
-26,random,0.0,0.2163
-27,random,0.0,0.4202
-28,random,0.0,0.1175
-29,random,0.0,0.2494
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-1,llama3,0.0,0.3636
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-11,llama3,0.0,0.1429
-12,llama3,0.0,0.1466
-13,llama3,0.0,0.3226
-14,llama3,0.0,0.1695
-15,llama3,0.0,0.25
-16,llama3,0.0,0.2381
-17,llama3,0.0,0.3391
-18,llama3,0.0,0.4386
-19,llama3,0.0,0.1639
-20,llama3,0.0,0.2909
-21,llama3,0.0,0.3077
-22,llama3,0.0,0.3906
-23,llama3,0.0,0.4
-24,llama3,0.0,0.1563
-25,llama3,0.0,0.2727
-26,llama3,0.0,0.2381
-27,llama3,0.0,0.2759
-28,llama3,0.0,0.1818
-29,llama3,0.0,0.2899
-30,llama3,0.0,0.2857
-1,mistral-small,0.0,0.1429
-2,mistral-small,0.0,0.1111
-3,mistral-small,0.0,0.1
-4,mistral-small,0.0,0.1111
-5,mistral-small,0.0,0.1111
-6,mistral-small,0.0,0.1
-7,mistral-small,0.0,0.1667
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-9,mistral-small,0.0,0.1309
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-11,mistral-small,0.0,0.1667
-12,mistral-small,0.0,0.125
-13,mistral-small,0.0,0.1
-14,mistral-small,0.0,0.1111
-15,mistral-small,0.0,0.2
-16,mistral-small,0.0,0.1111
-17,mistral-small,0.0,0.1111
-18,mistral-small,0.0,0.1111
-19,mistral-small,0.0,0.1493
-20,mistral-small,0.0,0.1429
-21,mistral-small,0.0,0.125
-22,mistral-small,0.0,0.1111
-23,mistral-small,0.0,0.125
-24,mistral-small,0.0,0.2
-25,mistral-small,0.0,0.1429
-26,mistral-small,0.0,0.1
-27,mistral-small,0.0,0.1111
-28,mistral-small,0.0,0.1111
-29,mistral-small,0.0,0.1111
-30,mistral-small,0.0,0.1111
-1,deepseek-r1, 0.0,0.1667
-2,deepseek-r1,0.0,0.2097
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-4,deepseek-r1,0.0,0.1905
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-6,deepseek-r1,0.0,0.1111
\ No newline at end of file
diff --git a/figures/investment/investment.svg b/figures/investment/investment.svg
index 7c81295..1edd557 100644
--- a/figures/investment/investment.svg
+++ b/figures/investment/investment.svg
@@ -6,7 +6,7 @@
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<cc:Work>
<dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
- <dc:date>2025-03-24T14:46:52.844601</dc:date>
+ <dc:date>2025-03-26T13:51:51.025345</dc:date>
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@@ -41,7 +41,7 @@ z
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<g id="text_1">
<!-- random -->
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<defs>
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L 416 3319
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<g id="xtick_2">
<g id="text_2">
<!-- llama3 -->
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<g id="xtick_3">
<g id="text_3">
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diff --git a/src/investment/investment.py b/src/investment/investment.py
index 4c54be5..e1104bd 100644
--- a/src/investment/investment.py
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@@ -24,7 +24,7 @@ class AgentResponse(BaseModel):
# The investment game simulation class
class Investment:
def __init__(self, model: str, temperature: float, max_retries: int = 3):
- self.debug = True
+ self.debug = False
self.model = model
self.temperature = temperature
self.strategy = random
@@ -159,39 +159,33 @@ class Investment:
"""
Computes the Critical Cost Efficiency Index (CCEI).
"""
- n = len(prices) # Number of observations
- c = [1] # Minimize theta
- A_ub = [] # Constraint matrix
- b_ub = [] # Right-hand side values
- for t in range(n):
- for s in range(n):
- lhs = np.dot(prices[t], choices[s]) # p_t * x_s
- rhs = np.dot(prices[t], choices[t]) # p_t * x_t
- if lhs > rhs: # Only add constraints where direct revealed preference exists
- A_ub.append([-budgets[t]]) # -theta * I_t
- b_ub.append(lhs - rhs)
- # Ensure A_ub is a valid 2D array
- if A_ub:
- A_ub = np.array(A_ub, dtype=float)
- if A_ub.ndim == 1: # Ensure it's 2D
- A_ub = A_ub.reshape(-1, 1)
- else:
- A_ub = np.zeros((1, 1), dtype=float) # If no constraints, use a trivial 1x1 matrix
- # Ensure b_ub is also valid
- b_ub = np.array(b_ub, dtype=float) if b_ub else np.zeros(1, dtype=float)
-
- bounds = [(0, 1)] # Theta bounds
- # Solve the linear program
- result = linprog(c, A_ub=A_ub, b_ub=b_ub, bounds=bounds, method="highs")
- if result.success:
- return round(result.x[0], 4) # Return optimized theta value
- else:
- print("CCEI computation failed. Check constraints.")
- return 0 # Return 0 if LP fails
+ num_rounds = len(prices)
+ lambdas = []
+ for i in range(num_rounds):
+ # Objective: Maximize lambda (minimize -lambda)
+ c = [-1]
+ # Constraints: p_t * x_s <= lambda * I_t for all rounds s
+ A = []
+ b = []
+ for j in range(num_rounds):
+ p_t = prices[i]
+ x_s = choices[j]
+ I_t = budgets[i]
+ A.append([p_t[0] * x_s[0] + p_t[1] * x_s[1]])
+ b.append(I_t)
+ # Add constraint that lambda is between 0 and 1
+ bounds = [(0, 1)]
+ # Solve the linear programming problem
+ res = linprog(c, A_ub=A, b_ub=b, bounds=bounds, method='highs')
+ if res.success:
+ lambdas.append(res.x[0])
+ else:
+ lambdas.append(0)
+ return min(lambdas) # The CCEI is the minimum lambda across all rounds
# Run the async function and return the response
if __name__ == "__main__":
game_agent = Investment(model="mistral-small", temperature=0.0) # Toggle strategy here
- response = asyncio.run(game_agent.run_rounds(10))
+ response = asyncio.run(game_agent.run_rounds(30))
print(response)
diff --git a/src/investment/investment_draw.py b/src/investment/investment_draw.py
index d2e47da..baa7ab3 100644
--- a/src/investment/investment_draw.py
+++ b/src/investment/investment_draw.py
@@ -4,7 +4,7 @@ import matplotlib.pyplot as plt
# Custom color palette
color_palette = {
- 'random': '#333333', #
+ 'random' : '#333333', # Black
'gpt-4.5-preview-2025-02-27': '#7abaff', # Blue
'llama3': '#32a68c', # Green
'mistral-small': '#ff6941', # Orange
diff --git a/src/investment/investment_experiments.py b/src/investment/investment_experiments.py
index ed828f0..a51056a 100644
--- a/src/investment/investment_experiments.py
+++ b/src/investment/investment_experiments.py
@@ -3,9 +3,9 @@ import csv
from investment import Investment # Assuming this is in a separate file
# Define models, temperature, and iterations
-models = ["optimal", "random"] # "gpt-4.5-preview-2025-02-27" "random", "llama3", "mistral-small", "deepseek-r1"
+models = ["optimal", "random", "llama3", "mistral-small", "deepseek-r1"] # "gpt-4.5-preview-2025-02-27", "optimal", "random", "llama3", "mistral-small", "deepseek-r1"
temperature = 0.0
-iterations = 10
+iterations = 30
output_file = "../../data/investment/investment.csv"
async def run_experiment():
@@ -22,7 +22,7 @@ async def run_experiment():
# Run DictatorConsistency experiment
game_agent = Investment(model=model, temperature=temperature)
- ccei_value = await game_agent.run_rounds(10) # Run 25 rounds
+ ccei_value = await game_agent.run_rounds(25) # Run 25 rounds
# Write results to CSV
writer.writerow([iteration, model, temperature, ccei_value])
--
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