If the sequence a = (a„>^ E /2, i.e., ||a||2 = 2~=0 | a„ |2 < oo, define Sa as the sequence of averages 1 " 2 ak n + 1 , It follows easily from the Marcinkiewicz Interpolation Theorem that S is a bounded operator from I2 to I2; this can also be proved directly using the Cauchy-Buniakowski-Schwarz inequality [1]. S is known as the Cesàro operator. S is, of course, not bounded below, but the foll...

We show that a real bounded sequence (xn) is Cesaro convergent to l if and only the of averages with indices in [αk,αk+1) converges for all α>1 . If, addition, (xn)...

I compare two information structures in a common value first-price auction with two bidders: In one, each of the two bidders knows only his own signal about the value of the object, and in the other, one of the bidders learns his opponent’s signal as well. Gaining the additional information in the second information structure makes the informed bidder worse off if the value is submodular in the...

We investigate the role of search frictions in markets with price competition and how it leads to sorting of heterogeneous agents. There are two aspects of value creation: the match-value when two agents actually trade, and the probability of trading governed by the search technology. We show that positive assortative matching obtains when complementarities in the former outweigh complementarit...

We study the Lov¶ asz extension b v for cooperative games v by using the marginal worth vectors and the dividends. First, we prove that the marginal worth vector aC with respect to an x-compatible ordering C satis ̄es, for supermodular games, b v(x) = min fhx; yi : y 2 Core(v)g = ­x; aC® : Next, we obtain the following characterization of the utility function of a market game: The utility functi...

Inspired by problems in data center scheduling, we study the submodularity of certain scheduling problems as a function of the set of machine capacities and the corresponding implications. In particular, we • give a short proof that, as a function of the excess vector, maximum generalized flow is submodular and minimum cost generalized flow is supermodular; • extend Wolsey’s approximation guara...

We study the ordinal content of assuming supermodularity, including conditions under which a binary relation can be represented by a supermodular function. When applied to revealed-preference relations, our results imply that supermodularity is some times not refutable: Choices on consumption at different prices can be rationalized with a supermodular utility if they can be rationalized. Hence,...

We study the ordinal content of assuming supermodularity, including conditions under which a binary relation can be represented by a supermodular function. When applied to revealed-preference relations, our results imply that supermodularity is some times not refutable: A consumer’s choices can be rationalized with a supermodular utility function if they can be rationalized with a monotonic uti...