Stable cooperation in differential games with random duration

The problem of time-consistency of cooperative solutions is investigated in the paper. This problem was stated by Petrosyan L.A. in 1977 for differential games with a finite time horizon. In this paper a modification of the game with a finite time horizon is considered, namely, the random time horizon of the game is supposed. The Shapley value is used as an optimality principle under cooperative behavior of players. For this formulation the definition of the imputation distribution procedure (IDP) is given and the analytic formula for IDP is derived. Moreover, the irrational behavior proofness condition by D.W.K. Yeung (2006) is modified for the problem with random duration. The tool is based on using IDP. Theoretical results are illustrated by an example of the differential game of non-renewable resource extraction.