Abstract
In stochastic control problems or in stochastic differential games the choice of an observation model is critical. In particular for control or game problems involving a random point process it is possible to consider the Fokker-Planck type of equation, and the process itself as the observation equation. In the context of the single-server queueing problem the state equation becomes p t = - (α t + β t ) p t + α t , where p t = prob, that the server is busy, α t = the rate parameter of the arrival process, controlled by one player, β t = the parameter of the service time, controlled by another player. This equation describes a bilinear system. Choosing a linear cost functional and a variety of associated point processes as observables, the conceptual problems of separation principles, existence of value, and saddle point solutions arise. The results obtained in this paper are shown to be applicable to the optimization of resource allocation systems that can be modeled as co-operative or competitive games. The martingale representation theorems play a central role in this discussion.
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© 1977 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Ephremides, A. (1977). Information Patterns in Stochastic Point Process Differential Games. In: Kožešnik, J. (eds) Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians, vol 7A. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9910-3_11
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DOI: https://doi.org/10.1007/978-94-010-9910-3_11
Publisher Name: Springer, Dordrecht
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