We consider the problem of online keyword advertising auctions among multiple bidders with limited budgets, and study a natural bidding heuristic in which advertisers attempt to optimize their utility by equalizing their return-on-investment across all keywords. We show that existing auction mechanisms combined with this heuristic can experience cycling (as has been observed in many current systems), and therefore propose a modified class of mechanisms with small random perturbations. This perturbation is reminiscent of the small time-dependent perturbations employed in the dynamical systems literature to convert many types of chaos into attracting motions. We show that the perturbed mechanism provably converges in the case of first-price auctions and experimentally converges in the case of second-price auctions. Moreover, the point of convergence has a natural economic interpretation as the unique market equilibrium in the case of first-price mechanisms. In the case of second-price auctions, we conjecture that it converges to the "supply-aware" market equilibrium. Thus, our results can be alternatively described as a tâtonnement process for convergence to market equilibrium in which prices are adjusted on the side of the buyers rather than * Work performed while author was an intern at Microsoft Research. † Work performed while author was a postdoc at Microsoft Research.
We prove the existence of a poly(n, m)-time computable pseudorandom generator which "1/poly(n, m)-fools" DNFs with n variables and m terms, and has seed length O(log 2 nm · log log nm). Previously, the best pseudorandom generator for depth-2 circuits had seed length O(log 3 nm), and was due to Bazzi (FOCS 2007).It follows from our proof that a 1/mÕ (log mn) -biased distribution 1/poly(nm)-fools DNFs with m terms and n variables. For inverse polynomial distinguishing probability this is nearly tight because we show that for every m, δ there is a 1/m Ω(log 1/δ) -biased distribution X and a DNF φ with m terms such that φ is not δ-fooled by X.For the case of read-once DNFs, we show that seed length O(log mn · log 1/δ) suffices, which is an improvement for large δ.It also follows from our proof that a 1/m O(log 1/δ) -biased distribution δ-fools all read-once DNF with m terms. We show that this result too is nearly tight, by constructing a 1/mΩ (log 1/δ) -biased distribution that does not δ-fool a certain m-term read-once DNF.
Abstract. Goldreich (ECCC 2000) proposed a candidate one-way function construction which is parameterized by the choice of a small predicate (over d = O(1) variables) and of a bipartite expanding graph of right-degree d. The function is computed by labeling the n vertices on the left with the bits of the input, labeling each of the n vertices on the right with the value of the predicate applied to the neighbors, and outputting the n-bit string of labels of the vertices on the right.Inverting Goldreich's one-way function is equivalent to finding solutions to a certain constraint satisfaction problem (which easily reduces to SAT) having a "planted solution," and so the use of SAT solvers constitutes a natural class of attacks.We perform an experimental analysis using MiniSat, which is one of the best publicly available algorithms for SAT. Our experiment shows that the running time required to invert the function grows exponentially with the length of the input, and that such an attack becomes infeasible already with small input length (a few hundred bits).Motivated by these encouraging experiments, we initiate a rigorous study of the limitations of back-tracking based SAT solvers as attacks against Goldreich's function. Results by Alekhnovich, Hirsch and Itsykson imply that Goldreich's function is secure against "myopic" backtracking algorithms (an interesting subclass) if the 3-ary parity predicate P (x1, x2, x3) = x1 ⊕ x2 ⊕ x3 is used. One must, however, use non-linear predicates in the construction, which otherwise succumbs to a trivial attack via Gaussian elimination.We generalized the work of Alekhnovich et al. to handle a more general class of predicates, and we present a lower bound for the construction that uses the predicate P d (x1, . . . , x d ) := x1 ⊕x2 ⊕· · ·⊕x d−2 ⊕(x d−1 ∧x d ) and a random graph.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.