In this paper, we consider a selfish bin packing problem, where each item is a selfish player and wants to minimize its cost. In our new model, if there are k items packed in the same bin, then each item pays a cost 1/k, where k ≥ 1. First we find a Nash Equilibrium (NE) in time O(n log n)...

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>