Ergodicity-Breaking Reveals Time Optimal Economic Behavior in Humans

Abstract

Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theory reveals 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 economic 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.

The ergodicity problem in economics

“…Not all individuals are the same, but an overall pattern is clearly seen. Data reproduced from ref 11. .…”

Microfoundations of Discounting

“…Our work contributes to the growing field of ergodicity economics (Peters 2019) in which decision makers maximize the long-time growth rate of resources, rather than expectation values of psychologically transformed resource flows (possibly under psychologically transformed probability measures). This study joins recent evidence of strong dependence on wealth dynamics of human decisions under uncertainty (Meder et al 2019) and may be used to design similar experiments without uncertainty.…”

Microfoundations of Discounting

“…Our work contributes to the growing field of ergodicity economics (Peters and Gell-Mann, 2016;Berman, Peters and Adamou, 2017;Peters and Adamou, 2018) in which decision makers maximize the long-time growth rate of resources, rather than expectation values of psychologicallytransformed resource flows (under, in prospect theory, psychologically-transformed probability measures). This study joins recent evidence of strong dependence on wealth dynamics of human decisions under uncertainty (Meder et al, 2019) and may be used to design similar experiments without uncertainty.…”