This paper discusses revenue inequalities, utility equivalence, and a model of competition in auction design in symmetric equilibrium of k-price auctions, <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$k\ge 1$</EquationSource> </InlineEquation>, all in the setup of symmetric independent-private-value auctions. Our recommendation to organizers of auctions is to conduct...</equationsource></inlineequation>

We study the least core, the kernel and bargaining sets of coalitional games with a countable set of players. We show that the least core of a continuous superadditive game with a countable set of players is a non-empty (norm-compact) subset of the space of all countably additive measures. Then...