Ergodicity-breaking reveals time optimal decision making in humans

TL;DR

This paper investigates how humans adapt their utility functions under different gamble dynamics, revealing that risk aversion aligns with time optimality predictions, which challenges existing decision theories.

Contribution

It demonstrates that human risk preferences are modulated by gamble dynamics in ways consistent with ergodic, time optimal decision-making, a novel insight beyond current theories.

Findings

Risk aversion increases under multiplicative dynamics.

Utility functions adapt to maximize time-average wealth growth.

Results challenge traditional decision theories.

Abstract

Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theories of decision-making reveal how individuals should tolerate risk in different environments. To optimise wealth over time, agents should adapt their utility function according to the dynamical setting they face. Linear utility is optimal for additive dynamics, whereas logarithmic utility is optimal for multiplicative dynamics. Whether humans approximate time optimal behavior across different dynamics is unknown. Here we compare the effects of additive versus multiplicative gamble dynamics on risky choice. We show that utility functions are modulated by gamble dynamics in ways not explained by prevailing decision theory. Instead, as predicted by time optimality, risk aversion increases under multiplicative dynamics, distributing close to the values that maximise the time average growth of wealth. We suggest that our findings motivate a need for explicitly grounding theories of decision-making on ergodic considerations.