The core of games on convex geometries

Article Abstract:

A study has been conducted to develop a model of cooperative games in which only certain coalitions are allowed to form. The structure of allowable coalitions have been studied using the theory of convex geometries. Findings have indicated a game on a convex geometry is a real-valued function defined on the family L of the closed sets of a closure operator which satisfies the finite Minkowski-Krein-Milman property. It has also been found that games on convex geometries, the Weber set is contained in the core if and only if the game is quasi-convex.

Operations Research, Management science, Game theory, Convex functions

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Unboundedness of a convex quadratic function subject to concave and convex quadratic constraints

Article Abstract:

The parameters for the upper and lower bounds on a convex quadratic function limited by both concave and convex quadratic constraints are discussed. These parameters should be satisfied for the upper bounds to exist under concave constraints. A method involving the solution of a finite number of special structure linear programs is also developed to determine if the conditions are met. In addition, an algorithm to solve the functions is formulated.

Quadratic programming, Equations, Quadratic, Quadratic equations

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