In game theory, basic solution concepts often conflict with experimental findings or intuitive reasoning. This fact is possibly due to the requirement that zero probability is assigned to irrational choices in these concepts. Here, we introduce the epistemic notion of common belief in utility...

Given a seller with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$k$$</EquationSource> </InlineEquation> types of items, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$m$$</EquationSource> </InlineEquation> of each, a sequence of users <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\{u_1, u_2,\ldots \}$$</EquationSource> </InlineEquation> arrive one by one. Each user is single-minded, i.e., each user is interested only in a particular bundle of items. The seller must set the price and assign some amount of bundles to each...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

New versions and extensions of Benson’s outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous...

This paper deals with the problem of scenario tree reduction for stochastic programming problems. In particular, a reduction method based on cluster analysis is proposed and tested on a portfolio optimization problem. Extensive computational experiments were carried out to evaluate the...