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Stable Cooperation in Differential Game with Random Time Horizon

Venerdi' 28 Gennaio 2011 - Ekaterina Shevkoplyas

ARGOMENTI: Seminari

Venerdi' 28 Gennaio 2011 alle ore 12:30 in aula 1BC50 Ekaterina Shevkoplyas (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University) terra' una conferenza dal titolo "Stable Cooperation in Differential Game with Random Time Horizon".

-Abstract
The differential game of non-renewable resource extraction on the base of the classical cake-eating modelis examined. The main focus of the paper is an application of the stable cooperation concept which includes time-consistency of the cooperative agreement (Petrosyan, 1977), strategic stability (Petrosyan, Zenkevich,2009) and irrational behavior proofness(Yeung, 2006) to the game of resource exploitation. At first I investigate the time-consistency, strategic stability and irrational behavior proofness for the classical model with n symmetric players.
Then I consider one modification of the game with elements of stochastic framework, in the sense that the terminal time T is a random value in order to increase the realness of the modeling. I suggest modified concept of the time-consistency and Yeung's condidtion which is suitable for the problem with random duration of the game. It is analytically proved that the results for games with random duration cover the results for deterministic games and games with constant discounting.
Then the cooperative model of the resource extraction game is examined for time-consistency, strategic stability and irrational behavior proofness under condition of Weibull distribution for the random terminal time T (Shevkoplyas, 2009; Shevkoplyas, 2010b). Accordingly to Weibull distribution shape parameter, the life circle of the non-renewable resource extraction such as an"infant" stage, "adult" stage and "aged" stage is described. The egalitarian solution is given and analyzed on cooperative stability conditions for all three stages of the game.
Finally, I consider another modifications of the differential game of resource extraction and research the time-consistency problem for new formulations.

-Keywords
differential games, random duration, resource extraction, stable cooperation, time-consistency, random duration, Weibull distribution

Rif. int. A. Buratto

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