Statistical Decision Theory and Game Theory (7 ECTS)

Basic concepts, decision rules and loss/risk functions, principles of dominance and admissibility, minimax principle, decision theory via classical statistics, loss functions (squared error, absolute, zero–one), properties of estimators under different loss functions, examples of inadmissible classical estimators, hypothesis tests as decision problems, Bayesian decision theory, prior and posterior distributions, conjugate families of distributions, Bayes risk and expected posterior risk and loss, Bayes estimators and posterior decision rules, relationship between Bayesian rules and admissibility, interpretation of Bayesian procedures, comparison of classical and Bayesian approaches, elements of game theory, normal-form games and payoff matrices, strategies and best responses, Nash equilibria, cooperative game theory, classic examples of game theory, applied decision theory, decision problems with loss and payoff matrices, case studies from economics, sports analytics, and public policy.

Recommended Reading:

• Berger, J. O. (1985) Statistical Decision Theory and Bayesian Analysis. 2nd Edition, Springer, New York (NY). http://dx.doi.org/10.1007/978-1-4757-4286-2
• Parmigiani, G. and Inoue, L. Y. T. (2009). Decision theory: Principles and approaches. John Wiley & Sons. https://doi.org/10.1002/9780470746684
• Παπασταμούλης, Π. (2019). Στοιχεία Θεωρίας Αποφάσεων. Πανεπιστημιακές σημειώσεις ΟΠΑ.
• Osborne, M. J. (2010). Εισαγωγή στη Θεωρία Παιγνίων. Εκδόσεις Κλειδάριθμος. Επιμέλεια ελληνικής έκδοσης: Ιωάννης Ρεφανίδης.  ISBN: 9789604613939. Κωδικός βιβλίου στον Εύδοξο: 35241.