David John Aldous (University of California)

Brouwer medal

Gambling under unknown probabilities as a proxy for real world decisions under uncertainty

We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known.  The framework, in gambling terms, is that the size of a bet is proportional to the gambler’s perceived advantage based on their perceived probability, and their accuracy in estimating true probabilities is measured by mean-squared-error.  Within this framework one can study the cost of estimation errors, and seek to formalize the “obvious” notion that in competitive  interactions between agents whose actions depend on their perceived  probabilities,  those who are more accurate at estimating probabilities will generally be more successful than those who are less accurate.  The mathematics in this talk is entirely elementary, but the conceptual background is more sophisticated.