The objective of this special issue of Applied Stochastic Models in Business and Industry is to introduce a new theme, the use of game theory and decision theory in reliability and risk analysis. In so doing, the special issue brings together novel research from disciplines that have a lot to contribute to this theme, including economics, engineering, finance, medical sciences, probability, and statistics. The issue contains six papers. Four of these papers were presented at the First Symposium on Games and Decisions in Reliability and Risk which was held at The George Washington University on May 27–28, 2009.
The discussion paper by David Banks, Francesca Petralia, and Shouqiang Wang introduces adversarial risk analysis as an alternative solution approach to game theory problems. The approach is implemented to gambling problems based on Borel games. The paper is discussed by Joseph B. Kadane and Nicholas G. Polson.
The paper by Ethem Çanakoglu and S üleyman Özekici considers optimal portfolio selection, where distributions of asset returns change according to a latent Markovian process. A dynamic programming approach is developed to obtain a characterization of the optimal portfolio policy under the resulting hidden Markov model.
Nader Ebrahimi, Ehsan S. Soofi, and Shaoqiong Zhao present properties of information measures for the Dirichlet family and related distributions. A new information characterization of the Dirichlet distribution in terms of survival and hazard gradient constraints is introduced.
The paper by Rabin E. J. Neslo and Roger M. Cooke introduces probabilistic inversion methods to characterize a population of stakeholders' preferences via a probability distribution of utilities. The method is suitable for multicriteria evaluation problems, where utilities are inferred using data from discrete choices. The methodology is applied for the evaluation of actual health states data.
Nicholas G. Polson and Morten Sorensen develop a simulation-based approach to stochastic dynamic programming problems. The presented approach is an alternative to the Q-learning algorithm of Watkins and Dayan (1992, Machine Learning, 8:279–292). The approach is illustrated using a dynamic investment problem.
Nozer D. Singpurwalla gives an expository perspective on mathematical issues associated with the failure rate. More specifically, the circumstances, where the exponentiation formula overestimates the probability of survival, are discussed. The point is illustrated using Volterra's product integrals.