TY - GEN

T1 - Game-theoretic probability and defensive forecasting

AU - Shafer, Glenn

PY - 2007

Y1 - 2007

N2 - In 2001, Vladimir Vovk and I demonstrated how game theory can replace measure theory as a foundation for classical probability theory, discrete and continuous {Probability and Finance: Its Only a Game!, Wiley 2001). In the game-theoretic framework, classical probability theorems are proven by betting strategies that make a player rich without risking bankruptcy if the theorem's prediction fails. These strategies can be specified explicitly, and so the theory has a constructive flavor that lends itself to applications in economics and statistics. Defensive forecasting is one of the most interesting of these applications. It identifies a comprehensive betting strategy, which becomes rich if the probabilities fail in a relevant way (say by being uncalibrated or having poor resolution), and it chooses probabilities to defeat this comprehensive betting strategy. The fact that this is possible gives us new insight into the very meaning of probability.

AB - In 2001, Vladimir Vovk and I demonstrated how game theory can replace measure theory as a foundation for classical probability theory, discrete and continuous {Probability and Finance: Its Only a Game!, Wiley 2001). In the game-theoretic framework, classical probability theorems are proven by betting strategies that make a player rich without risking bankruptcy if the theorem's prediction fails. These strategies can be specified explicitly, and so the theory has a constructive flavor that lends itself to applications in economics and statistics. Defensive forecasting is one of the most interesting of these applications. It identifies a comprehensive betting strategy, which becomes rich if the probabilities fail in a relevant way (say by being uncalibrated or having poor resolution), and it chooses probabilities to defeat this comprehensive betting strategy. The fact that this is possible gives us new insight into the very meaning of probability.

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U2 - 10.1109/WSC.2007.4419612

DO - 10.1109/WSC.2007.4419612

M3 - Conference contribution

AN - SCOPUS:49749149164

SN - 1424413060

SN - 9781424413065

T3 - Proceedings - Winter Simulation Conference

SP - 272

EP - 280

BT - Proceedings of the 2007 Winter Simulation Conference, WSC

T2 - 2007 Winter Simulation Conference, WSC

Y2 - 9 December 2007 through 12 December 2007

ER -