Boris Model: On the Theory of Infinite Step Processes of Sequential Decision Making

Shalom,
The next meeting of the seminar in Logic, Set Theory and Topology will hold on Tuesday, November 27. Time is 16:00 – 17:30.
Place: seminar room 201 which is located in the building of Computer Science Department (not Math Dept)

Speaker: Boris Model(BGU)

Title: “On the Theory of Infinite Step Processes of Sequential Decision Making”
Abstract: On the border of Set Theory and Game Theory there is a broad class of Infinite Step  Processes of Sequential Decision Making that can be characterized by the main following property: a Future development of the process depends on the process Present state and does not depend directly on the process Past [1] (these processes have the same nature as for example chess and checkers have: a game Future depends on the game Present state and does not depend directly on the game Past).
Some examples of such Infinite Step Processes give us Differential Games in certain posing [2] and Infinite Stage Games of Search and Completion [3,4].
For these Processes with the use of Axiom of Choice some generalizations of basic results, which are well known facts in case of Finite Step Decision Making Processes (for example, existence of a uniformly optimal strategy), can be proved [1,2].
But the question when information about process Past additional to knowledge of process Present state is important for these Infinite Step Processes from the point of view of process optimal result and when this additional information is not important has remained an open question (for Finite Step Decision Making Processes like chess and checkers such additional information is not important but for some of these Infinite Step Processes it is important [1]).

References
1. B. I. Model’, The existences of an overall έ-optimal strategy and validity of Bellman’s functional equation in an extended class of dynamic processes. I; II, Engineering  Cybernetics, No.5, 1975, pp. 13 – 19; No. 6, 1975, pp. 12 – 19.
2. B. I. Model’, A certain class of differential games, Engineering Cybernetics, No.2, 1978, pp. 32 – 38.
3. B. I. Model’, Games of search and completion, Journal of Mathematical Sciences, Vol. 80, No 2, 1996, pp. 1699 – 1744, Plenum Publishing Corporation, New York.
4. U. Abraham, R. Schipperus, Infinite games on finite sets, Israel Journal of
Mathematics 159, 2007, pp. 205-219.

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