Geodesic
Time-consistency Problem Under Condition of a Random Game Duration in Resource Extraction
Contributions to game theory and management, Tome 2 (2009), pp. 461-473

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We consider time-consistency problem for cooperative differential $n$-person games with random duration. It is proved, that in many cases the solution (or optimality principle) for such games is time-inconsistent. For regularization of solution the special imputation distributed procedure (IDP) is introduced and the time-consistency of the new regularized optimality principle is proved. At last we consider one game-theoretical problem of non-renewable resource extraction under condition of a random game duration. The problem of time-consistency for the Shapley Value in this example is investigated.
Keywords: time-consistency, random duration, Shapley Value, differential game, non-renewable resource. 
@article{CGTM_2009_2_a34,
     author = {Ekaterina V. Shevkoplyas},
     title = {Time-consistency {Problem} {Under} {Condition} of a {Random} {Game} {Duration} in {Resource} {Extraction}},
     journal = {Contributions to game theory and management},
     pages = {461--473},
     publisher = {mathdoc},
     volume = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2009_2_a34/}
}
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Ekaterina V. Shevkoplyas. Time-consistency Problem Under Condition of a Random Game Duration in Resource Extraction. Contributions to game theory and management, Tome 2 (2009), pp. 461-473. http://geodesic.mathdoc.fr/item/CGTM_2009_2_a34/