Dynamic Core of Fuzzy Dynamical Cooperative Games
Aubin, Jean-Pierre (2005), Dynamic Core of Fuzzy Dynamical Cooperative Games, in Nowak, Andrzej; Szajowski, Krzysztof, Advances in Dynamic Games. Applications to Economics, Finance, Optimization, and Stochastic Control, Springer : Berlin, p. 129-162. http://dx.doi.org/10.1007/0-8176-4429-6_7
Book titleAdvances in Dynamic Games. Applications to Economics, Finance, Optimization, and Stochastic Control
Book authorNowak, Andrzej; Szajowski, Krzysztof
Series titleAnnals of the International Society of Dynamic Games
Number of pages679
MetadataShow full item record
Abstract (EN)We use in this paper the viability/capturability approach for studying the problem of characterizing the dynamic core of a dynamic cooperative game defined in a characteristic function form. In order to allow coalitions to evolve, we embed them in the set of fuzzy coalitions. Hence, we define the dynamic core as a set-valued map associating with each fuzzy coalition and each time the set of allotments is such that their payoffs at that time to the fuzzy coalition are larger than or equal to the one assigned by the characteristic function of the game. We shall characterize this core through the (generalized) derivatives of a valuation function associated with the game. We shall provide its explicit formula, characterize its epigraph as a viable-capture basin of the epigraph of the characteristic function of the fuzzy dynamical cooperative game, use the tangential properties of such basins for proving that the valuation function is a solution to a Hamilton-Jacobi-Isaacs partial differential equation and use this function and its derivatives for characterizing the dynamic core.
Subjects / KeywordsHamilton-Jacobi-Isaacs partial differential equation; fuzzy coalitions; dynamic core; dynamic cooperative game
Showing items related by title and author.