A Game with Program Control and Variable Terminal Moment
AbstractIn the theory of positional differential games, it is well known that continuous strategies, generally speaking, do not provide the best possible result. In the present paper, a simple example is given that shows that a similar property holds for conflict control systems in which one of the two players chooses a program control, and the other one chooses the moment of termination of the game, in which the payoff is calculated. The payoff functional depends on the phase state of this time moment. It is shown that in this control system no rule for choosing the terminal time time moment described by a continuous mapping can guarantee the corresponding player a nonzero result. Two examples of such discontinuous rules are given. One of them requires measuring the phase at one time moment only.
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Bibliographic InfoPaper provided by International Institute for Applied Systems Analysis in its series Working Papers with number ir99044.
Date of creation: Sep 1999
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This paper has been announced in the following NEP Reports:
- NEP-ALL-1999-10-13 (All new papers)
- NEP-GTH-1999-10-04 (Game Theory)
- NEP-IND-1999-10-13 (Industrial Organization)
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