Time-subinterval shifting in zero-sum games played in staircase-function finite and uncountably infinite spaces

Document Type : Original paper

Author

Faculty of Mechanical and Electrical Engineering, Polish Naval Academy, Gdynia, Poland

Abstract

A tractable and efficient method of solving zero-sum games played in staircase-function finite spaces is presented, where the possibility of varying the time interval on which the game is defined is considered. The time interval can be narrowed by an integer number of time subintervals and still the solution is obtained by stacking solutions of smaller-sized matrix games, each defined on a subinterval where the pure strategy value is constant. The stack is always possible, even when only time is discrete and the set of pure strategy possible values is uncountably infinite. So, the solution of the initial discrete-time staircase-function zero-sum game can be obtained by stacking the solutions of the ordinary zero-sum games defined on rectangle, whichever the time interval is. Any combination of the solutions of the subinterval games is a solution of the initial zero-sum game.

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References

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Communications in Combinatorics and Optimization
Volume 8, Issue 4
December 2023
Pages 603-629

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