# Bayesian regret

In stochastic game theory, Bayesian regret is the expected difference ("regret") between the utility of a Bayesian strategy and that of the optimal strategy (the one with the highest expected payoff).

The term Bayesian refers to Thomas Bayes (1702–1761), who proved a special case of what is now called Bayes' theorem, who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as Bayesian inference.

## Economics

This term has been used to compare a random buy-and-hold strategy to professional traders' records. This same concept has received numerous different names, as the New York Times notes:

"In 1957, for example, a statistician named James Hanna called his theorem Bayesian Regret. He had been preceded by David Blackwell, also a statistician, who called his theorem Controlled Random Walks.[1] Other, later papers had titles like 'On Pseudo Games',[2] 'How to Play an Unknown Game'[3][citation needed], 'Universal Coding'[4] and 'Universal Portfolios'".[5][6]

## References

1. ^ Controlled random walks, D Blackwell, Proceedings of the International Congress of Mathematicians 3, 336-338
2. ^ Banos, Alfredo (December 1968). "On Pseudo-Games". The Annals of Mathematical Statistics. 39 (6): 1932–1945. doi:10.1214/aoms/1177698023. ISSN 0003-4851.
3. ^ Harsanyi, John C. (1982), "Games with Incomplete Information Played by "Bayesian" Players, I–III Part I. The Basic Model", Papers in Game Theory, Dordrecht: Springer Netherlands, pp. 115–138, doi:10.1007/978-94-017-2527-9_6, ISBN 978-90-481-8369-2, retrieved 2023-06-13
4. ^ Rissanen, J. (July 1984). "Universal coding, information, prediction, and estimation". IEEE Transactions on Information Theory. 30 (4): 629–636. doi:10.1109/TIT.1984.1056936. ISSN 1557-9654. S2CID 206735464.
5. ^ Cover, Thomas M. (January 1991). "Universal Portfolios". Mathematical Finance. 1 (1): 1–29. doi:10.1111/j.1467-9965.1991.tb00002.x. ISSN 0960-1627. S2CID 219967240.
6. ^ Kolata, Gina (2006-02-05). "Pity the Scientist Who Discovers the Discovered". The New York Times. ISSN 0362-4331. Retrieved 2017-02-27.