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Mathematics 2018, 6(9), 165; https://doi.org/10.3390/math6090165

Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration

1
Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, St. Petersburg 198504, Russia
2
MEMOTEF, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 25 July 2018 / Revised: 24 August 2018 / Accepted: 31 August 2018 / Published: 11 September 2018
(This article belongs to the Special Issue Mathematical Game Theory)
Full-Text   |   PDF [363 KB, uploaded 11 September 2018]   |  

Abstract

A nonrenewable resource extraction game model is analyzed in a differential game theory framework with random duration. If the cumulative distribution function (c.d.f.) of the final time is discontinuous, the related subgames are differentiated based on the position of the initial instant with respect to the jump. We investigate properties of optimal trajectories and of imputation distribution procedures if the game is played cooperatively. View Full-Text
Keywords: differential games; non zero-sum games; cooperative games; resource extraction; random duration; IDP procedure differential games; non zero-sum games; cooperative games; resource extraction; random duration; IDP procedure
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Gromova, E.; Malakhova, A.; Palestini, A. Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration. Mathematics 2018, 6, 165.

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