In this paper we investigate the optimal supply function for a generator who sells electricity into a wholesale electricity spot market and whose profit function is not smooth. In previous work in this area, the generator’s profit function has usually been assumed to be continuously...

Game tree search is the core of most attempts to make computers play games. We present a fairly general theoretical analysis on how leaf evaluation errors influence the value estimation of a game position at the root. By an approach using prime factorization arguments in the ring of polynomials,...

A class of N-person stochastic games of resource extraction with discounted payoffs in discrete time is considered. It is assumed that transition probabilities have special additive structure. It is shown that the Nash equilibria and corresponding payoffs in finite horizon games converge as...

In this note we use the Shapley value to define a valuation function. A valuation function associates with every non-empty coalition of players in a strategic game a vector of payoffs for the members of the coalition that provides these players’ valuations of cooperating in the coalition. The...

This paper is focused on approximate ( <InlineEquation ID="IEq19"> <EquationSource Format="TEX">$$\varepsilon$$</EquationSource> </InlineEquation>-efficient) solutions of multiobjective mathematical programs. We introduce a new <InlineEquation ID="IEq20"> <EquationSource Format="TEX">$$\varepsilon$$</EquationSource> </InlineEquation>-efficiency concept which extends and unifies different notions of approximate solution defined in the literature. We characterize these <InlineEquation ID="IEq21"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

We consider a perturbed mathematical programming problem where both the objective and the constraint functions are polynomial in all underlying decision variables and in the perturbation parameter <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$\varepsilon.$$</EquationSource> </InlineEquation> We study the behaviour of the solutions of such a perturbed problem as <InlineEquation ID="IEq1"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation>