Journal of Optimization Theory and Applications

, Volume 172, Issue 1, pp 328–347 | Cite as

Looking Forward Approach in Cooperative Differential Games with Uncertain Stochastic Dynamics



In this study, a novel approach for defining and computing a solution for a differential game is presented for a case, wherein players do not have complete information about the game structure for the full time interval. At any instant in time, players have certain information about the motion equations and payoff functions for a current subinterval, and a forecast about the game structure for the rest of the time interval. The forecast is described by stochastic differential equations. The information about the game structure updates at fixed instants of time and is completely unknown in advance. A new solution is defined as a recursive combination of sets of imputations in the combined truncated subgames that are analyzed by the Looking Forward Approach. An example with a resource extraction game is presented to demonstrate a comparison of payoff functions without a forecast and that with stochastic and deterministic forecasts.


Differential game Looking Forward Approach Imputation distribution procedure Time consistency Strong time consistency 

Mathematics Subject Classification

49N70 91A12 



The first author acknowledges Saint-Petersburg State University for the research Grant No. The work of the second author was supported by Saint-Petersburg State University, Project 6.37.349.2015 and


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Saint-Petersburg State UniversitySaint-PetersburgRussia

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