We consider an exchange economy with time-inconsistent consumers whose preferences are additively separable. When these consumers trade in a sequence of markets, their time-inconsistency may introduce a non-convexity that gives them an incentive to trade lotteries. If there are many consumers, competitive equilibria with and without lotteries exist. The existence of symmetric equilibria may req...

In the study of the algebra NCSym of symmetric functions in noncommutative variables, Bergeron and Zabrocki found a free generating set consisting of power sum symmetric functions indexed by atomic partitions. On the other hand, Bergeron, Reutenauer, Rosas, and Zabrocki studied another free generating set of NCSym consisting of monomial symmetric functions indexed by unsplitable partitions. Can...

The literature has demonstrated that second-price common-value auctions are sensitive to the presence of asymmetries among bidders. In a two-bidder model, Bikhchandani [1988. Reputation in repeated second-price auctions. J. Econ. Theory 46, 97–119] has shown that if it is common knowledge that one bidder has a disadvantage compared to her opponent, that bidder (almost surely) never wins the auc...

Astract We study here the ring QSn of Quasi-Symmetric Functions in the variables x1, x2, . . . , xn. F. Bergeron and C. Reutenauer [4] formulated a number of conjectures about this ring, in particular they conjectured that it is free over the ring Λn of symmetric functions in x1, x2, . . . , xn. We present here an algorithm that recursively constructs a Λn-module basis for QSn thereby proving o...

We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite extension of spherically symmetric equilibria, which covers all these models simultaneously. In the Vlasov case the equilibria are characterized by a local ...

We give a basis for the space spanned by the sumˆs λ of the lowest degree terms in the expansion of the Schur symmetric functions s λ in terms of the power sum symmetric functions p µ , where deg(p i) = 1. These lowest degree terms correspond to minimal border strip tableaux of λ. The dimension of the space spanned byˆs λ , where λ is a partition of n, is equal to the number of partitions of n ...