School of Mathematical Sciences

A discourse on decision theory menu

A discourse on decision theory

Ole Peters (London Mathematical Laboratory)
Tue, 11/03/2014 - 16:30
Seminar series: 

In April 2010 I gave a seminar at the Santa Fe Institute where I demonstrated that certain classic problems in economics can be resolved by re-visiting basic tenets of the formalism of decision theory. Specifically, I noted that simple mathematical models of economic processes, such as the random walk or geometric Brownian motion, are non-ergodic. Because of the non-stationarity of the processes, observables cannot be assumed to be ergodic, and this leads to a difference in important cases between time averages and ensemble averages. In the context of decision theory, the former tend to indicate how an individual will fare over time, while the latter may apply to collectives but are a priori meaningless for individuals. The effects of replacing expectation values by time averages are staggering -- realistic predictions for risk aversion, market stability, and economic inequality follow directly. This observation led to a discourse with Murray Gell-Mann and Kenneth Arrow about the history and development of decision theory, where the first studies of stochastic systems were carried out in the 17th century, and its relation to the development of statistical mechanics where refined concepts were introduced in the 19th century. I will summarize this discourse and present my current understanding of the problems.