Books, classic papers, and foundational references related to ergodicity economics.
37 publications
Poundstone, W. (2025). Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street (Expanded 20th anniversary ed.). Picador. ISBN 978-1-250-39112-4.
The twentieth-anniversary edition of this definitive work on the Kelly criterion was expanded to include an account of ergodicity economics.
Vanhoyweghen, A., Ginis, V., & Macharis, C. (2025). Beyond expected travel time: Unveiling the role of ergodicity breaking in mobility decisions and effective transportation policy. Transportation Research Interdisciplinary Perspectives, 34, 101663.
Uses thought experiments to show how non-ergodic travel times and absorbing boundaries can make reliability more important than expected speed, with implications for modal-shift policy.
Vanhoyweghen, A., Macharis, C., & Ginis, V. (2025). Investigating the origins of redistributive behaviour in non-ergodic contexts. Proceedings of the Royal Society A, 481(2326), 20250598.
Uses stated-preference experiments with multiplicative gambles to show that redistributive choices can reflect self-interested time-average growth and risk management rather than altruism alone.
Peters, O., & Adamou, A. (2025). An Introduction to Ergodicity Economics. LML Press. ISBN 978-1-0686491-3-4.
A one-semester textbook placing the ergodicity question at the centre of economic decision-making.
Verbruggen, B., Vanhoyweghen, A., & Ginis, V. (2025). Reinforcement learning in path-dependent, non-ergodic contexts. Proceedings of the Royal Society A, 480(2314), 20240415.
Introduces a temporal training mechanism that lets reinforcement-learning agents account for path dependence and optimize time-average performance in non-ergodic settings, including a portfolio problem related to the Kelly criterion.
Baumann, D., Noorani, E., Price, J., Peters, O., Connaughton, C., & Schon, T. B. (2025). Reinforcement learning with non-ergodic reward increments: robustness via ergodicity transformations. Transactions on Machine Learning Research.
Applies ergodicity transformations to reinforcement learning with non-ergodic reward increments, aiming for more robust individual-trajectory performance.
Vanhoyweghen, A., & Ginis, V. (2023). Human decision-making in a non-ergodic additive environment. Proceedings of the Royal Society A, 479(2278), 20230544.
Shows experimentally that decision-makers adjust their risk aversion in additive dynamics according to their distance from an absorbing ruin boundary, consistent with sensitivity to non-ergodicity and time-average outcomes.
Fant, L., Mazzarisi, O., Panizon, E., & Grilli, J. (2023). Stable cooperation emerges in stochastic multiplicative growth. Physical Review E, 108, L012401.
Investigates stability of cooperative protocols in stochastic multiplicative growth.
Peters, O. (2023). Insurance as an ergodicity problem. Annals of Actuarial Science, 17(2), 237-240.
A concise actuarial-science framing of insurance as a non-ergodic wealth-growth problem.
Peters, O., & Adamou, A. (2022). The ergodicity solution of the cooperation puzzle. Philosophical Transactions of the Royal Society A, 380, 20200425.
Shows how repeated pooling and sharing can raise time-average growth by reducing effective fluctuations, offering a baseline mechanism for cooperation.
Vanhoyweghen, A., Verbeken, B., Macharis, C., & Ginis, V. (2022). The influence of ergodicity on risk affinity of timed and non-timed respondents. Scientific Reports, 12, 3744.
Uses stated-choice experiments to test whether time pressure changes decisions under additive and multiplicative dynamics.
Adamou, A., Berman, Y., Mavroyiannis, D., & Peters, O. (2021). Microfoundations of discounting. Decision Analysis, 18(4), 257-272.
Derives discounting behavior from decision criteria and dynamics, connecting intertemporal choice to time-average growth reasoning.
Meder, D., Rabe, F., Morville, T., Madsen, K. H., Koudahl, M. T., Dolan, R. J., Siebner, H. R., & Hulme, O. J. (2021). Ergodicity-breaking reveals time optimal decision making in humans. PLOS Computational Biology, 17(9), e1009217.
An experimental test of whether human risk preferences shift with additive versus multiplicative dynamics.
Berman, Y., & Kirstein, M. (2021). Risk preferences in time lotteries. arXiv:2108.08366.
Applies growth-optimal reasoning to lotteries over payment time and compares it with expected discounted utility theory.
Berman, Y., Peters, O., & Adamou, A. (2021). Wealth inequality and the ergodic hypothesis: evidence from the United States. Journal of Income Distribution, 30(1).
Tests whether a standard wealth-dynamics model equilibrates quickly enough for the ergodic hypothesis to be useful in US wealth-inequality data.
Gigerenzer, G. (2021). Axiomatic rationality and ecological rationality. Synthese, 198, 3547-3564.
Examines axiomatic and ecological approaches to rationality and how each evaluates decisions.
Peters, O. (2020). Comment on D. Bernoulli (1738)
Specifies the difference between Bernoulli's 1738 decision theory and expected utility theory.
Peters, O., Adamou, A., Kirstein, M., & Berman, Y. (2020). What are we weighting for? A mechanistic model for probability weighting. Researchers.One.
Reinterprets probability weighting as a possible response to uncertainty about probabilities estimated from time series.
Peters, O. (2019). The ergodicity problem in economics. Nature Physics, 15, 1216-1221.
The broad Nature Physics overview that gave the field its clearest public formulation.
Fisher, A. J., Medaglia, J. D., & Jeronimus, B. F. (2018). Lack of group-to-individual generalizability is a threat to human subjects research. Proceedings of the National Academy of Sciences, 115(27), E6106-E6115.
Compares within-person and between-person correlations across six intensive longitudinal datasets, showing that group estimates can poorly represent individual dynamics and motivating explicit tests of generalizability.
Stollmeier, F., & Nagler, J. (2018). Unfair and anomalous evolutionary dynamics from fluctuating payoffs. Physical Review Letters, 120(5), 058101.
Shows how temporal variation and covariance in payoffs can systematically favor one strategy, producing unexpected cooperation in the prisoner’s dilemma and reversing selection in the hawk–dove game.
Peters, O., & Adamou, A. (2018). The time interpretation of expected utility theory. arXiv:1801.03680.
Develops the correspondence between utility functions and ergodicity transformations for wealth dynamics.
Peters, O., & Gell-Mann, M. (2016). Evaluating gambles using dynamics. Chaos, 26, 023103.
A compact statement of the ergodicity economics decision-theory perspective: specify dynamics, then evaluate time-average growth.
Peters, O. (2011). The time resolution of the St Petersburg paradox. Philosophical Transactions of the Royal Society A, 369(1956), 4913-4931.
Recasts the St Petersburg paradox as a problem of time averages versus expectation values.
Peters, O. (2011). Optimal leverage from non-ergodicity. Quantitative Finance, 11(11), 1593-1602.
Shows how non-ergodicity in multiplicative finance dynamics leads to a finite optimal leverage and clarifies the limits of ensemble-average reasoning.
Peters, O. (2011). Menger 1934 revisited. Manuscript.
Revisits Karl Menger's critique of Bernoulli's logarithmic resolution of the St Petersburg paradox and identifies mathematical errors in Menger's argument.
Molenaar, P. C. M. (2004). A manifesto on psychology as idiographic science: Bringing the person back into scientific psychology, this time forever. Measurement: Interdisciplinary Research and Perspectives, 2(4), 201-218.
Explains why group-level patterns generally cannot be assumed to describe individual dynamics unless strict ergodicity conditions hold, and argues for idiographic analysis in psychology.
Bouchaud, J.-P., & Mezard, M. (2000). Wealth condensation in a simple model of economy. Physica A, 282, 536-545.
Introduces a simple stochastic exchange model with multiplicative dynamics, Pareto wealth tails, and a transition between broad inequality and more evenly spread wealth.
Radner, R. (1998). Economic survival. In D. P. Jacobs, E. Kalai, & M. I. Kamien (Eds.), Frontiers of Research in Economic Theory: The Nancy L. Schwartz Memorial Lectures, 1983-1997 (pp. 183-209). Cambridge University Press.
Developed from Radner's Nancy L. Schwartz Memorial Lecture at Northwestern University, this chapter examines economic survival and firm failure as objectives that standard profit- and utility-maximizing models largely neglect.
Kacelnik, A., & Bateson, M. (1997). Risk-sensitivity: Crossroads for theories of decision-making. Trends in Cognitive Sciences, 1(8), 304-309.
Reviews normative and process-based accounts of animal decision-making under risk, including budget-dependent predictions, risk preferences for variable delays and reward amounts, and the case for theoretical plurality.
Algoet, P. H., & Cover, T. M. (1988). Asymptotic optimality and asymptotic equipartition properties of log-optimum investment. The Annals of Probability, 16(2), 876–898.
Extends Breiman’s growth-optimality result beyond independent, identically distributed returns: a portfolio that maximizes conditional expected log return at each step is asymptotically optimal for arbitrary market processes.
Arthur, W. B., Ermoliev, Y. M., & Kaniovskii, Y. M. (1983). A generalized urn problem and its applications. Cybernetics, 19(1), 61–71. https://doi.org/10.1007/BF01070110
Early use of a non-ergodic model (generalized Polya urns) for modelling an economic process (technological adoption).
Thorp, E. O. (1975). Portfolio choice and the Kelly criterion. In W. T. Ziemba & R. G. Vickson (Eds.), Stochastic Optimization Models in Finance (pp. 599–619). Academic Press.
Extends the Kelly–Breiman framework to portfolios with changing investment opportunities, continuous returns, and some dependence across periods, and contrasts long-run growth optimality with mean–variance analysis.
Breiman, L. (1961). Optimal Gambling Systems for Favorable Games. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1, 65-78.
Connects favorable repeated gambling to long-run growth, making explicit the time-average logic behind optimal betting systems.
Kelly, J. L. Jr. (1956). A New Interpretation of Information Rate. The Bell System Technical Journal, 35(4), 917-926.
Introduces the growth-optimal betting criterion, a central predecessor of time-average reasoning in finance and decision theory.
Whitworth, W. A. (1886). Choice and chance: An elementary treatise on permutations, combinations, and probability, with 640 exercises. Cambridge: Deighton, Bell & Co.
A nineteenth-century introduction to combinatorics and probability built around worked problems and an extensive collection of exercises.
Bernoulli, D. (1954 [1738]). Exposition of a New Theory on the Measurement of Risk. Econometrica, 22(1), 23-36.
The canonical origin of expected utility theory, and therefore an essential foil for ergodicity economics.
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