Hilbert series and Hilbert depth of squarefree Veronese ideals

In this paper, we obtain explicit formulas for the Hilbert series and Hilbert depth of squarefree Veronese ideals in a standard graded polynomial ring.Comment: 7 pages, a gap in the previous version is fixe

Interchange fee rate, merchant discount rate and retail prices in a credit card network: A game-theoretic analysis

We consider two game-theoretic settings to determine the optimal values of an issuer's interchange fee rate, an acquirer's merchant discount rate, and a merchant's retail price in a credit card network. In the first setting, we investigate a two-stage game problem in which the issuer and the acquirer first negotiate the interchange fee rate, and the acquirer and the retailer then determine their merchant discount rate and retail price, respectively. In the second setting, motivated by the recent US bill “H.R. 2695,” we develop a three-player cooperative game in which the issuer, the acquirer, and the merchant form a grand coalition and bargain over the interchange fee rate and the merchant discount rate. Following the cooperative game, the retailer makes its retail pricing decision. We derive both the Shapley value- and the nucleolus-characterized, and globally-optimal unique rates for the grand coalition. Comparing the two game settings, we find that the participation of the merchant in the negotiation process can result in the reduction of both rates. Moreover, the stability of the grand coalition in the cooperative game setting may require that the merchant should delegate the credit card business only to the issuer and the acquirer with sufficiently low operation costs. We also show that the grand coalition is more likely to be stable and the U.S. bill “H.R. 2695” is thus more effective, if the degree of division of labor in the credit card network is higher as the merchant, acquirer, and issuer are more specialized in the retailing, acquiring, and issuing operations, respectively. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 201

A fair staff allocation rule for the capacity pooling of multiple call centers

We construct a cooperative staffing game to investigate how to fairly allocate a reduced number of staff among multiple call centers that pool (centralize) their capacities. We show that this game is essential and submodular, and, thereby, convex with a non-empty core. We also propose a neat Shapley value-characterized staff-allocation rule, which exists in the core of the game