Plenary Lecture

Criteria of Strategic Behaviour and Optimum Trajectories for the Problem of Sequential Decision

Associate Professor Ilie Mitran
Vice-Rector
University of Petrosani
Romania
E-mail: iliemitran@gmail.com

Abstract: The results of this paper are obtained starting from the formulation, in a generalized form, of a sequential decisional problem, related to which we suggest the solving of the following issues:
1. the determination of the optimum criteria for certain strategic behavior types of decision makers;
2. the specification of the conditions for which this criteria are equivalent;
3. the determination of certain important properties for the optimum trajectories;
4. establishing the conditions for which a decision maker can get and maintain an advantageous situation.
The strategic behavior of decision makers is analyzed considering the two existing possibilities: cautious strategic behavior and hazardous strategic behavior. In the case of decision makers having hazardous strategic behavior, there are analyzed all the optimum criteria which are already known with a specific view on certain relatively new and less studied criteria such as maximum probability criterion and different variants of entropic criteria.
In the case of cautious strategic behavior, the paper focuses on the maximum stability principle (with all variants of equilibrium solutions, maxmin solutions, minmax solutions) and the equalization principle (a relatively new and less studied criterion). The paper also analyses different qualitative situations which can appear while carrying out the decisional process: non-cooperative situations, partial cooperative situations and total cooperative situations. In the cases of partial cooperative and total cooperative situations, a new coalition criterion in the cooperative games theory is brought forward, namely the coalition in the sense of maximum probability. Within the cooperative game theory, there are two basic issues: the way coalitions are formed and the way payoffs are distributed to players. This new form of coalition allows the utility transfer and it is more general than the criterion based upon the concepts of characteristic function and imputation. Moreover, this form of coalition admits the determination of an optimal distribution of payoffs by solving an optimal problem which has an entropic efficiency criterion.
The theoretical results obtained are used in order to solve some major technical-economical problems: the analysis of systems' reliability, the analysis of the stability of mining works, the determination of some forecasting indicators, problems of ruination and financial arbitrage etc.

Brief Biography of the Speaker:
Ilie Mitran graduated from the University of Timisoara in 1975, receiving the 5 years Diploma in Mathematics, specialization Operations Research. Five years later (1980) he has graduated from the Economic Studies Academy, receiving the 5 years Diploma in Economics, specialization in Cybernetics and Economic Planning. He joined in 1980 the University of Petrosani, Romania. In 1988, he received the Ph.D. in Mathematics, based upon the doctoral thesis “Mathematical Contributions regarding Cybernetic Modeling of the Decisional Process”. The extended version of the doctoral thesis was published in France with the title “Co–operative and Partial Co–operative Decisional Models”, AMSE Publishing House, 1990. In 1998, he received the second Ph. D. in Engineering with the doctoral thesis “Contributions regarding the Systems Renewal Modeling”. In 1992 he became Associated Professor of Applied Mathematics. He is a member of American Mathematical Society (AMS - SUA), Association for the Advancement of Modeling and Simulation Techniques in Enterprises (AMSE - France), Society for Industrial and Applied Mathematics (SIAM - SUA), Mathematical Association of America (MAA - SUA). He is also a member of the International Advisory Board for The Academic Periodical Publication of the Faculty of Economics at the University of Miskolc. His general research interests are: Applied Mathematics, Decision Modeling, Econometrics, Operations Research.
He published 9 books, more than 80 paper in various scientific journals and international conference proceedings.
He served as the Dean of Faculty of Science, between 2000-2008. Nowadays, he serves as the Vice – Rector of the University of Petrosani.