279 research outputs found
A potential approach to solutions for set games
No full textConcerning the solution theory for set games, the paper introduces a new solution by allocating, to any player, the items (taken from an universe) that are attainable for the player, but can not be blocked (by any coalition not containing the player). The resulting value turns out to be an utmost important concept for set games to characterize the family of set game solutions that possess a so-called potential representation (similar to the potential approaches applied in both physics and cooperative game theory). An axiomatization of the new value, called Driessen--Sun value, is given by three properties, namely one type of an efficiency property, the substitution property and one type of a monotonocity property
Coincidence of and collinearity between game theoretic solutions
No full textThe first part is the study of several conditions which are sufficient for the coincidence of the prenucleolus concept and the egalitarian nonseparable contribution (ENSC-) method. The main sufficient condition for the coincidence involved requires that the maximal excesses at the ENSC-solution are determined by the (n-1)-person coalitions in then-person game. The second part is the study of both a new type of games, the so-calledk-coalitionaln-person games, and the interrelationship between solutions on the class of those games. The main results state that the Shapley value of ak-coalitionaln-person game can be written as a convex or affine combination of the ENSC-solution and the centre of the imputation set
Contributions to the theory of cooperative games: the t-value and k-convex games
No full textContains fulltext :
mmubn000001_029006899.pdf (Publisher’s version ) (Open Access)Promotores : S. Tijs en M. Maschler179 p
Convexity and the Shapley value in Bertrand oligopoly TU-games with Shubik's demand functions
No full textThe Bertrand Oligopoly situation with Shubik's demand functions is modelled as a cooperative TU game. For that purpose two optimization problems are solved to arrive at the description of the worth of any coalition in the so-called Bertrand Oligopoly Game. Under certain circumstances, this Bertrand oligopoly game has clear affinities with the well-known notion in statistics called variance with respect to the distinct marginal costs. This Bertrand Oligopoly Game is shown to be totally balanced, but fails to be convex unless all the firms have the same marginal costs. Under the complementary circumstances, the Bertrand Oligopoly Game is shown to be convex and in addition, its Shapley value is fully determined on the basis of linearity applied to an appealing decomposition of the Bertrand Oligopoly Game into the difference between two convex games, besides two nonessential games. One of these two essential games concerns the square of one non- essential game.Bertrand Oligopoly situation, Bertrand Oligopoly Game, Convexity, Shapley Value, Total Balancedness.
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