We consider a setting where in a known future time, a certain continuous random variable will be realized. There is a public prediction that gradually converges to its realized value, and an expert that has access to a more accurate prediction. Our goal is to study when should the expert reveal his information, assuming that his reward is based on a logarithmic market scoring rule (i.e., his reward is proportional to the gain in log-likelihood of the realized value).

We analyze the expert's optimal policy when allowed (1) a single prediction (2) multiple predictions. In the single-prediction case we characterize the expert's optimal policy and show that it is threshold based. We analyze the expert's asymptotic expected optimal reward and show a tight connection to the Law of the Iterated Logarithm. For multiple predictions we show that truthfulness and making as many predictions as allowed are best policy.

Joint work with Yossi Azar & Yishay Mansour

Bio:

Amir Ban received his BSc from the Technion, Haifa, in 1978. He devoted the next 3 decades to a career as a developer, inventor and entrepreneur, during which, in 1986, he obtained an MSc from the Technion, Haifa. After working for several Israeli high-tech companies, in 1991 he became a founder of M-Systems, participating in pioneering the then-nascent flash memory technology, including the invention of USB flash drives in 1999. In parallel, he devoted many years to computer chess, authoring the program Junior AKA Deep Junior. In Paris 1997 Junior won its first world championship, and in Yokohama 2013, its eighth. Returning to academia in 2008, he received his PhD in 2014 from the Hebrew University at the Centre for Rationality. He is since doing post-doctorate research in Tel-Aviv University. He is the recipient of the 2015 IEEE Information Storage Systems Award.