No clear distinction was made between the two mathematical objects, which can be interpreted as an implicit assumption of ergodicity.
It emphasizes the physical meaning of expected values as averages across a statistical ensemble of parallel systems.
Non-ergodicity is closely related to the problems of irreversibility and path dependence[2] that are common themes in economics.
In mathematics and physics, the concept of ergodicity is used to characterise dynamical systems and stochastic processes.
In doing so it builds on existing critiques of the use of expected value in the modeling of economic decisions.
For instance, expected-utility theory was proposed in 1738 by Daniel Bernoulli[3] as a way of modeling behavior which is inconsistent with expected-value maximization.
[4] The ergodicity economics research programme originates in two papers by Ole Peters in 2011, a theoretical physicist and current external professor at the Santa Fe Institute.
[5] The first studied the problem of optimal leverage in finance and how this may be achieved by considering the non-ergodic properties of geometric brownian motion.
From this follows a possible decision theory where agents maximize the time-average growth rate of wealth.
An influential class of models for economic decision-making is known as expected utility theory.
The following specific model can be mapped to the growth-rate optimization highlighted by ergodicity economics.
A non-linear utility function allows the encoding of behavioral patterns not represented in expected-value maximization.
simply implements a preference for faster utility growth in the expected-utility-theory decision protocol.
Stochastic processes other than (3) possess different ergodicity transformations, where growth-optimal agents maximize the expected value of utility functions other than the logarithm.
[11] It demonstrates how an expected-value analysis can indicate that a gamble is favorable although the gambler is guaranteed to lose over time.
In this thought experiment, discussed in,[8] a person participates in a simple game where they toss a fair coin.
This calculation shows that the game is favorable in expectation—its expected value increases with each round played.
, provides a characteristic scalar which can be compared with the per-round growth factor of the expected value.
The comparison between expected value and time-average performance illustrates an effect of broken ergodicity: over time, with probability one, wealth decreases by about 5% per round, in contrast to the increase by 5% per round of the expected value.
Markets are not ergodic because sequences of events cannot be simply represented by long-term statistical averages.
In December 2020, Bloomberg news published an article titled "Everything We’ve Learned About Modern Economic Theory Is Wrong"[14] discussing the implications of ergodicity in economics following the publication of a review of the subject in Nature Physics.
[15] In the book Skin in the Game, Nassim Nicholas Taleb suggests that the ergodicity problem requires a rethinking of how economists use probabilities.
[17] In the book The End of Theory, Richard Bookstaber lists non-ergodicity as one of four characteristics of our economy that are part of financial crises, that conventional economics fails to adequately account for, and that any model of such crises needs to take adequate account of.
[citation needed] In the book The Ergodic Investor and Entrepreneur, Boyd and Reardon tackle the practical implications of non-ergodic capital growth for investors and entrepreneurs, especially for those with a sustainability, circular economy, net positive, or regenerative focus.
[19] James White and Victor Haghani discuss the field of ergodicity economics in their book The Missing Billionaires.
In the example the long-term growth rate favors the certain loss and seems an inappropriate criterion for the short-term decision horizon.
Finally, an experiment by Meder and colleagues claims to find that individual risk preferences change with dynamical conditions in ways predicted by ergodicity economics.
[22] Doctor, Wakker, and Tang criticize the experiment for being confounded by differences in ambiguity and the complexity of probability calculations.
Further, they criticize the analysis for applying static expected utility theory models to a context where dynamic versions are more appropriate.
In support of this, Goldstein claims to show that multi-period EUT predicts a similar change in risk preferences as observed in the experiment.