Game On
A Foreword to the Art & Science of Better Decisions.
Abstract
This essay examines the evolution of decision-making theories, from ancient philosophical views on judgment to modern economic models. It explores the limitations of traditional frameworks, such as the Rational Expectations Hypothesis and behavioural economics, particularly their failure to address the complexities of human learning under uncertainty and shortcomings in their research design. The essay highlights the importance of the Rational Beliefs Hypothesis in understanding how economic agents form beliefs in the face of uncertainty. Drawing on these insights, it suggests that adopting a multidisciplinary perspective could provide a more nuanced understanding of human decision-making under uncertainty.
Introduction
The pursuit of sound judgement has captivated the minds of philosophers, psychologists, and scientists since the era of ancient Greek civilisation, dating back to approximately 1200 BCE.
The early reflections of thinkers such as Seneca, Aurelius, and Socrates posited that our judgements are the sole domain over which we truly wield control. Consequently, much of their philosophical discourse centred on living well and the ‘right action’ across varying circumstances.
Centuries later, Sigmund Freud, the progenitor of psychoanalysis, advanced his theory of the unconscious. His work - which explored the tension between conscious control and unconscious impulses - posited that repressed desires, especially those tied to sexuality and early childhood experiences, manifest indirectly through dreams, slips of the tongue ("Freudian slips"), and neurotic behaviours. Dreams, in particular, were considered by Freud to be a "royal road to the unconscious,"[1] revealing hidden conflicts and unfulfilled wishes. Freud’s innovative clinical practice, which he later named psychoanalysis, offered a markedly different lens through which to view human behaviour.
Like the teachings of early philosophers, Freud’s ideas have gradually fallen out of favour as society has evolved. Advances in technology and scientific understanding have reshaped our view of the mind, moving away from frameworks rooted in introspection and subjective interpretation.
A Brief Tour of the Landscape
My interest in human judgment has been shaped by a deep curiosity about how systems characterised by uncertainty influence our decision-making. This fascination is not merely academic; as an active investor, I grapple with these uncertainties daily, where each decision reflects an attempt to navigate and interpret the complex interplay of probabilities and risks inherent in the markets.
However, by studying more generalised models of the economy we can analyse the conditions under which the decisions of economic agents are optimal in the sense that market clearing prices exist. Such a broad class of models can then be readily extended to incorporate - and analyse - the effects of asset markets on the decisions of economic agents.
A survey[2] of the literature shows that there are only a few theories that attempt to explain how economic agents— a person, company, or organisation that impacts the economy by producing, buying, or selling goods and services— make decisions.
General Competitive Analysis
Of these, General Competitive Analysis and, later, the Rational Expectations Hypothesis are the central theories used to establish the presence of market clearing prices.
Unfortunately both are overly simplified versions of reality. The former lacked a coherent explanation of how expectations are formulated and the latter assume all investors are omniscient in that they know the demand and supply functions of all market participants, how to extract present and future general equilibrium prices and the stochastic law of motion of the economy over time.
Their impact on academia and practitioners has lasted for decades, giving rise to numerous PhDs, books, and several generations of consultants. This enduring influence can be attributed to two key factors: the underlying mathematical frameworks of standard Overlapping Generations (OLG) models are well-documented and straightforward to work with, and there is an assumption—explicit or implicit—that disequilibrium learning analysis can uncover locally unique rational expectations equilibria.
However, standard OLG models with fiat money are characterised by a multitude of rational expectations solution paths. Each path, indexed by a different initial price level, could serve as a valid representation of the economy. These models typically exhibit two steady states:
1. Autarkic steady state: In this state, real money balances have no value.
2. Monetary steady state: Here, real money balances hold positive value.
Nearly all solution paths involve a price level that increases indefinitely, eventually converging to the autarkic steady state. The sole exception is the solution path that starts with a price level equal to the monetary steady state, which stabilises at this level.
The monetary steady state is thus considered a determinate steady state, as it has a locally unique solution path. In contrast, the autarkic steady state is an indeterminate steady state, as it lacks a locally unique solution path. Within any small neighbourhood of the autarkic steady state, multiple solution paths can exist, all of which remain close to it.
Duffy (1994)[3] shows that disequilibrium learning rules can cause agents to adopt beliefs about non-stationary, indeterminate equilibria that are locally stable. As a result, the convergence of a particular learning rule to a specific unique solution does not guarantee that learning behaviour will universally lead agents to the same solution.
Behavioural Economics
Behavioural economics represents an early attempt to map how the brain makes decisions of varying complexity. It is largely a descriptive theory that seeks to explain human decision-making through an experimental approach.
Over the course of my career, I have observed this theory evolve from a promising idea into a modern-day hydra. Today, behavioural economics is far from being a coherent theory. It is characterised by numerous contradictory models and lacks a unified explanation of human decision-making, aside from the observation that we are, at times, somewhat irrational. This absence of a normative framework—one that prescribes how humans should make decisions—undermines its practical utility.
For instance, are individuals more influenced by what they encounter first (anchoring) or by what they encounter most recently[4] (recency)?
Moreover, the field relies heavily on flawed experimental design. Its conclusions are frequently drawn from studies involving inexperienced participants—typically Western-educated students from wealthy, industrialised, and democratic nations. This is compounded by the disconcerting reality that many of its seminal findings cannot be replicated[5].
Although I was supportive of behavioural economics in its formative years, the statistician in me harboured doubts about its research methodology, which has failed to mature. Today, it is difficult to take seriously any claim that “we can do better,” particularly when, more than forty years after Kahneman and Tversky’s pioneering work on prospect theory, meaningful attention is only now being directed towards robust experimental design.
Rational Beliefs
The Rational Beliefs Hypothesis characterises the conditions that permit a diversity of beliefs to arise. The key ideas behind this theory is best explained with the aid of a simple example[6]. Define the present value of future dividends payable by a stock as:
Where:
⁃ λ is constant discount factor and
⁃ Ct is the dividends expected at time t.
Agents who observe the data need to evaluate the risky prospect of . However, the agents do not know the true probability distribution of the random sequence. They do, however, have a considerable amount of past data, from which they learn as much as possible to form beliefs about the conditional probabilities of the future sequence of random variables.
Kurz (1994)[7] established criteria for determining whether an agent’s probability beliefs are rational. His work assumes that agents formulate their beliefs by observing the history of data generated by the economy. The analysis shows how the frequencies with which events occur converge, in the limit, to a stationary probability measure. The main idea is that agents cannot learn the true probability distribution that generates the dynamic system. But they can learn the limiting stationary probability measure generated by the system.
Agents are assumed to lack detailed knowledge of the underlying dynamics that produce economic data. As a result, they do not automatically adopt the system's stationary probability measure as their belief. However, the analysis reveals that any stable dynamical system—such as one based on an agent’s beliefs—creates its own stationary probability measure, which depends on the probabilities within that belief system. This measure is independent of the data produced by the actual dynamical system. A belief system is considered rational if its stationary probability measure matches the stationary probability measure of the true dynamical system.
In a key application of the theory of rational beliefs, Kurz (1994) demonstrates that agents can express their uncertainty about the true probability distribution that generates the data by reflecting on the beliefs held by other market participants. This finding has significant implications for agents trading in the market. Instead of solely attempting to learn the true stationary probability measure generated by the economy, they may also choose to learn the distribution of beliefs that influences market pricing at any given time.
In a significant development of the theory, Nielsen (1996)[8] demonstrates that limit points of all converging sequences of rational beliefs are not necessarily part of the set of rational beliefs. To address this, Nielsen (1996) introduces restrictions on the set of admissible rational beliefs. These restrictions are:
The relative frequencies of observed events must converge uniformly to the stationary measure generated by the agent’s belief system over their finite investment horizon.
The probability of any cylinder (a finite-dimensional set) occurring must be non-zero.
With these restrictions in place, Nielsen (1996) proves that the resulting set of rational beliefs is closed under the topology of weak convergence.
The theory of rational beliefs ensures that the range of variation in each trader’s expectations remains limited, as each trader selects their rational belief from a compact set. While this approach elegantly addresses the technical challenges involved in proving the existence of a short-run Walrasian equilibrium, it excludes the possibility that biased expectations significantly influence the current price-formation process. However, since agents can hold diverse beliefs that align with the data, endogenous uncertainty cannot be ignored. As a result, the price-formation process in a rational belief economy is inherently more volatile than in a rational expectations economy.
A Way Forward
For three decades, I have focused on identifying—and, if possible, capitalising on—episodes of correlated endogenous beliefs—beliefs that appear to be biased relative to approximations of the market's stationary probability measure.
Over time, however, I began to feel that there might be something deeper at play, an idea that slowly developed from intuition into a vague sense at the edge of my awareness. To truly understand this, I recognise that I will need a mindset and toolkit far broader than the technicalities of short-run Walrasian equilibria or the complex task of extracting alpha from the markets.
Venturing beyond my immediate expertise could allow me to build broader connections and make incremental strides in deepening my understanding. Additionally, gaining a better understanding of how humans make decisions might enable me to design more effective decision-making processes.
Glossary
Autarkic Steady State
A theoretical state in which an economy or agent does not engage in trade with others and is entirely self-sufficient. In this state, economic agents rely solely on their own resources, and money or trade does not play a role.
Behavioural Economics
A subfield of economics that incorporates psychological insights into economic theory to explain why individuals and institutions often make decisions that deviate from the predictions of traditional economic models, which assume rational decision-making. Behavioural economics emphasises factors like cognitive biases, emotional influences, and social preferences.
Disequilibrium Learning
A process in which agents update their beliefs and expectations in an environment that is not in equilibrium. This concept challenges the assumption in traditional models that agents always operate in equilibrium, instead allowing for the possibility that agents’ beliefs and actions adjust over time in response to market disequilibria.
Market Clearing Prices
Prices at which the quantity of goods or services supplied equals the quantity demanded. In general equilibrium models, markets clear when all agents are satisfied with the prices, resulting in no excess supply or demand in any market.
Monetary Steady State
A steady state in which money has positive value and plays an active role in facilitating trade. In contrast to the autarkic steady state, the monetary steady state allows for the use of money to exchange goods and services, with money functioning as a store of value and medium of exchange.
Overlapping Generations Model (OLG)
An economic model that represents different generations of individuals who interact in markets. Each generation lives for two periods (young and old) and makes decisions based on its life cycle. OLG models are used to study intergenerational issues, such as savings, public debt, and the role of money.
Rational Beliefs Hypothesis
A theoretical framework that characterises the conditions under which agents form beliefs about uncertain outcomes in a way that is consistent with the stationary probability measure of a dynamic system. Unlike standard expectations models, agents are assumed to learn from historical data and may not have perfect knowledge of the system, but their beliefs are considered rational if they converge to the true stationary distribution.
Rational Expectations Hypothesis (REH)
A theory in economics that assumes agents form expectations about the future that are, on average, correct. In other words, agents’ forecasts reflect the true underlying economic model, and over time, errors in expectations are eliminated. REH assumes that market participants use all available information efficiently and that their predictions do not systematically deviate from the actual outcomes.
Stationary Probability Measure
A probability distribution that remains constant over time within a dynamic system. In the context of the Rational Beliefs Hypothesis, a stationary probability measure represents the long-term distribution towards which agents’ beliefs converge as they observe the system’s dynamics.
Walrasian Equilibrium
A state of the economy in which all markets clear simultaneously, meaning that supply equals demand in every market. Prices adjust to ensure that there is no excess supply or demand, and all economic agents are optimally choosing their consumption and production plans.
[1]. Freud, S. (1900) The Interpretation of Dreams.
[2]. Du Preez, J. (2003) Price Formation under Conditions of Uncertainty.
[3]. Duffy J (1994): “On Learning and the Nonuniqueness of Equilibrium in an Overlapping Generations Model with Fiat Money” Journal of Economic Theory, vol. 64, pp 541 – 553.
[4]. Smets, K. (2018). There is more to behavioural economics than biases and fallacies. Behavioural Scientist. Retrieved October 15, 2018.
[5]. Resnick B. (2018). The Stanford prison experiment was massively influential. We just learned it was a fraud.
[6]. Du Preez, J. (2003) Price Formation under Conditions of Uncertainty.
[7]. Kurz, M (1994): “On the Structure and Diversity of Rational Beliefs”Economic Theory, vol 4, no. 3, pp 877 to 900 (1994).
[8]. Nielsen C.K. (1996): “On Some Topological Properties of Stable Measures” Economic Theory 8, 531-553.
Interesting read Johan