Empirically testing a relationship between cooperation and the prime numbers.

Area of Science:

• Behavioral Economics
• Game Theory
• Number Theory

Background:

• Theoretical models link cooperation to prime numbers in evolutionary game theory.
• Similar patterns observed in predator-prey population dynamics with prime-numbered life cycles.

Purpose of the Study:

• To empirically test if cooperation in human public goods games exhibits cyclicality at prime-numbered time intervals.
• To assess the validity of theoretical predictions regarding prime-number cycles and cooperation.

Main Methods:

• Analysis of previously published data from human public goods games played across multiple time points.
• Statistical examination for cyclical patterns at prime-numbered intervals and placebo tests.

Main Results:

• Modest evidence of cyclicality at prime-numbered intervals was found, with rough agreement with theoretical predictions.
• Individual decisions showed increased contributions at prime-numbered time points, with a low chance of spurious estimation.
• Excluding low-value prime-numbered time points reduced the effect size, preventing rejection of the null hypothesis.

Conclusions:

• The hypothesis of increased cooperation at prime-numbered time points is cast into doubt for human public goods games.
• The observed effects appear driven by low-value prime-numbered time points, contrary to theoretical expectations.
• Empirical findings do not strongly support the theoretical models linking prime-number cycles to enhanced cooperation in this context.