run length and adapt vs. average risk adjustment

• how long does hawk/dove multi risk attitude take to converge with the new logic?
  • how many do not converge ?
• what difference does it make if we use adapt or average risk adjustment strategy?

---

Most recent analysis based on data generated with this command:

./simulatingrisk/hawkdovemulti/batch_run.py --params risk_adjust

Ran some tests with more iterations; when 200 iterations were specified, the percent of simulations that converged were closer to 85%, but all batches tested were in the 80% range.

import polars as pl

df = pl.read_csv("../../data/hawkdovemulti/riskadjust/dist-uniform/2025-08-05T153548_956082_model.csv")

total_runs = len(df)

print(f"Analyzing {total_runs} runs")

Analyzing 600 runs

simulation run length

They either finished very quickly (~50 steps) or never finished)

df["Step"].describe()

shape: (9, 2)

statistic	value
str	f64
"count"	600.0
"null_count"	0.0
"mean"	278.398333
"std"	363.777872
"min"	50.0
"25%"	61.0
"50%"	101.0
"75%"	200.0
"max"	1000.0

df["Step"].plot.hist()

# what about those that converged?

converged = df.filter(pl.col("status") == "converged")

converged["Step"].plot.hist()

what % converged?

status_totals = df["status"].value_counts()
status_totals

shape: (2, 2)

status	count
str	u32
"converged"	481
"running"	119

converg_total = status_totals.filter(status_totals["status"] == "converged")["count"][0]

print(f"{converg_total} runs out of {total_runs}; {converg_total/total_runs*100:.2f}% complete")

481 runs out of 600; 80.17% complete

risk adjustment (adopt / average)

hypothesis: adjustment strategy does not have a significant impact on the final result, only affects how long it takes to get there

from scipy import stats


df_riskadjust = converged.clone()

# TODO: make reusable functions for annotating data

for i in range(0, 10):
    # calculate new series based on existing 
    pct_risk_category = df_riskadjust.select(pl.col(f"total_r{i}") / pl.col("total_agents"))
    # add new column to the dataframe
    df_riskadjust = df_riskadjust.with_columns(pl.Series(name=f"pct_r{i}", values=pct_risk_category))

df_riskadjust = df_riskadjust.with_columns(
    pl.Series('pct_risk_inclined', values=df_riskadjust.select((pl.col("total_r0") + pl.col("total_r1") + pl.col("total_r2")) / pl.col("total_agents"))),
    pl.Series('pct_risk_moderate', values=df_riskadjust.select((pl.col("total_r3") + pl.col("total_r4") + pl.col("total_r5") + pl.col("total_r6")) / pl.col("total_agents"))),
    pl.Series('pct_risk_avoidant', values=df_riskadjust.select((pl.col("total_r7") + pl.col("total_r8") + pl.col("total_r9")) / pl.col("total_agents")))
)

df_riskadjust = df_riskadjust.with_columns(pl.Series('risk_attitude_mean', values=df_riskadjust.select(
        (pl.col("total_r1") + pl.col("total_r2")*2 + pl.col("total_r3")*3 + pl.col("total_r4")*4 + pl.col("total_r5")*5 + pl.col("total_r6")*6 + pl.col("total_r7")*7 + pl.col("total_r8")*8 + pl.col("total_r9")*9)  
         / pl.col("total_agents"))))


df_adopt = df_riskadjust.filter((pl.col("risk_adjustment") == "adopt"))
df_avg = df_riskadjust.filter((pl.col("risk_adjustment") == "average"))

print(f"adopt: {len(df_adopt):,} rows")
print(f"average: {len(df_avg):,} rows")

adopt: 251 rows
average: 230 rows

maxlen = min(len(df_adopt), len(df_avg))

stats.ttest_rel(df_adopt.select("pct_risk_inclined")[:maxlen], df_avg.select("pct_risk_inclined")[:maxlen])

TtestResult(statistic=array([0.30599364]), pvalue=array([0.75988749]), df=array([229]))

import altair as alt

alt.Chart(df_riskadjust).mark_boxplot().encode(
    x=alt.X('pct_risk_inclined', title='% risk inclined'), y=alt.Y('risk_adjustment', title="Adjustment"))

from simulatingrisk.hawkdovemulti import analysis_utils

# df_adopt, df_average

adopt_chart = analysis_utils.graph_population_risk_category(
    analysis_utils.groupby_population_risk_category(df_adopt)
).properties(title="risk adjust: adopt")
                                                                                                                                  
average_chart = analysis_utils.graph_population_risk_category(
    analysis_utils.groupby_population_risk_category(df_avg)
).properties(title="risk adjust: average")

(adopt_chart | average_chart).properties(title="distribution of population category by run").resolve_scale(y='shared')

Simulations that converged

# filter to status = running
converged = converged.with_columns(
    pct_agents_risk_changed=pl.col("num_agents_risk_changed").truediv(pl.col("total_agents")),
    seven_pct_pop=pl.col("total_agents").mul(0.07)
)

alt.Chart(converged).mark_boxplot().encode(
    x=alt.X('num_agents_risk_changed', title='# Agents that adjusted risk attitude'), 
    y=alt.Y('risk_adjustment', title='Adjustment')).facet('grid_size')

alt.Chart(converged).mark_boxplot().encode(
    x=alt.X('pct_agents_risk_changed', title='% of Agents that adjusted risk attitude'), 
    y=alt.Y('risk_adjustment', title='Adjustment')).facet('grid_size')

converg_pop_boxplot = alt.Chart(converged).mark_boxplot().encode(
    x=alt.X('sum_risk_level_changes', title='Total risk attitude changes'), 
    y=alt.Y('risk_adjustment', title='Adjustment'))

converg_pop_boxplot.facet('grid_size')

converg_threshold = alt.Chart(converged).mark_point(color="orange").encode(
    x="seven_pct_pop",
    y=alt.Y('risk_adjustment', title='Adjustment')
)
(converg_pop_boxplot + converg_threshold).facet('grid_size')

Simulations that did not converge

# filter to status = running
not_converged = df.filter(pl.col("status") == "running").with_columns(
    pct_agents_risk_changed=pl.col("num_agents_risk_changed").truediv(pl.col("total_agents")),
    seven_pct_pop=pl.col("total_agents").mul(0.07)
)

How many simulations with each adjustment type did not converge?

alt.Chart(not_converged).mark_bar().encode(
    y=alt.Y('risk_adjustment', title="Adjustment"), x='count(RunId)')

How many agents adjusted on the last adjustment round?

alt.Chart(not_converged).mark_boxplot().encode(
    x=alt.X('num_agents_risk_changed', title='# Agents that adjusted risk attitude'), 
    y=alt.Y('risk_adjustment', title='Adjustment'))

alt.Chart(not_converged).mark_boxplot().encode(
    x=alt.X('pct_agents_risk_changed', title='% of Agents that adjusted risk attitude'), 
    y=alt.Y('risk_adjustment', title='Adjustment'))

What about total population adjustments?

nonconverg_pop_boxplot = alt.Chart(not_converged).mark_boxplot().encode(
    x=alt.X('sum_risk_level_changes', title='Total risk attitude changes'), 
    y=alt.Y('risk_adjustment', title='Adjustment'))

nonconverg_pop_boxplot

Facet by grid size, and add a marker (orange circle) to indicate the threshold (based on 7% of total population size).

converg_threshold = alt.Chart(not_converged).mark_point(color="orange").encode(
    x="seven_pct_pop",
    y=alt.Y('risk_adjustment', title='Adjustment')
)
(nonconverg_pop_boxplot + converg_threshold).facet('grid_size')