Berlin 2018 – wissenschaftliches Programm

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 3: Economic Models I

SOE 3.3: Vortrag

Montag, 12. März 2018, 11:00–11:15, MA 001

Repeated gambles with uncertain parameters — •Mark Kirstein¹, Alexander Adamou², and Ole Peters^2,3 — ¹Economics Department, TU Dresden — ²London Mathematical Laboratory — ³Santa Fe Institute

Gambles repeated multiplicatively create non-ergodic changes in the gambler's wealth. The growth-optimal bet fraction maximises the time-average growth rate of his wealth or, equivalently, expected changes in his logarithmic utility. Standard treatments use models in which the gambler knows with certainty the parameters (i.e. the payoffs and probabilities) of the gamble. Here we confront the theoretically appealing results of such analyses with reality outside the model world. A realistic environment is one about which the gambler has some ignorance, manifested as uncertainty in his estimate of the gamble parameters. We build a simple model of this uncertainty, in addition to the more familiar uncertainty in the gamble's outcome. We find that a gambler maximising the time-average growth rate of his wealth under such conditions would bet a lower fraction of his wealth than anticipated by an observer making a conventional analysis, which assumes the gamble parameters are known. Indeed, it would look to this observer as if a gambler were weighing probabilities non-linearly, a psychological bias identified by behavioural economists as inconsistent with all models of rationality. Our approach, conversely, explains the gambler's behaviour as consistent with a straightforward optimisation strategy through time that accounts for his ignorance about the environment, for which no psychological assumptions are needed.