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On an approach to constructing a characteristic function in cooperative differential games

  • Mathematical Game Theory and Applications
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Abstract

We propose a novel approach to constructing characteristic functions in cooperative differential games. A characteristic function of a coalition S is computed in two stages: first, optimal control strategies maximizing the total payoff of the players are found, and next, these strategies are used by the players from the coalition S, while the other players, those from N S, use strategies minimizing the total payoff of the players from S. The characteristic function obtained in this way is superadditive. In addition, it possesses a number of other useful properties. As an example, we compute values of a characteristic function for a specific differential game of pollution control.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    E. V. Gromova & L. A. Petrosyan

Authors
  1. E. V. Gromova
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  2. L. A. Petrosyan
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Correspondence to E. V. Gromova.

Additional information

Original Russian Text © E.V. Gromova, L.A. Petrosyan, 2015, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2015, No. 4, pp. 19–39.

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Gromova, E.V., Petrosyan, L.A. On an approach to constructing a characteristic function in cooperative differential games. Autom Remote Control 78, 1680–1692 (2017). https://doi.org/10.1134/S0005117917090120

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  • DOI: https://doi.org/10.1134/S0005117917090120

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