44,143 research outputs found

    Self-stabilizing uncoupled dynamics

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    Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player's behavior is independent of the other players' preferences. Recognizing an equilibrium in this setting is a distributed computational task. Self-stabilizing uncoupled dynamics, then, have both resilience to arbitrary initial states and distribution of knowledge. We study these dynamics by analyzing their behavior in a bounded-recall synchronous environment. We determine, for every "size" of game, the minimum number of periods of play that stochastic (randomized) players must recall in order for uncoupled dynamics to be self-stabilizing. We also do this for the special case when the game is guaranteed to have unique best replies. For deterministic players, we demonstrate two self-stabilizing uncoupled protocols. One applies to all games and uses three steps of recall. The other uses two steps of recall and applies to games where each player has at least four available actions. For uncoupled deterministic players, we prove that a single step of recall is insufficient to achieve self-stabilization, regardless of the number of available actions

    On Revenue Monotonicity in Combinatorial Auctions

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    Along with substantial progress made recently in designing near-optimal mechanisms for multi-item auctions, interesting structural questions have also been raised and studied. In particular, is it true that the seller can always extract more revenue from a market where the buyers value the items higher than another market? In this paper we obtain such a revenue monotonicity result in a general setting. Precisely, consider the revenue-maximizing combinatorial auction for mm items and nn buyers in the Bayesian setting, specified by a valuation function vv and a set FF of nmnm independent item-type distributions. Let REV(v,F)REV(v, F) denote the maximum revenue achievable under FF by any incentive compatible mechanism. Intuitively, one would expect that REV(v,G)REV(v,F)REV(v, G)\geq REV(v, F) if distribution GG stochastically dominates FF. Surprisingly, Hart and Reny (2012) showed that this is not always true even for the simple case when vv is additive. A natural question arises: Are these deviations contained within bounds? To what extent may the monotonicity intuition still be valid? We present an {approximate monotonicity} theorem for the class of fractionally subadditive (XOS) valuation functions vv, showing that REV(v,G)cREV(v,F)REV(v, G)\geq c\,REV(v, F) if GG stochastically dominates FF under vv where c>0c>0 is a universal constant. Previously, approximate monotonicity was known only for the case n=1n=1: Babaioff et al. (2014) for the class of additive valuations, and Rubinstein and Weinberg (2015) for all subaddtive valuation functions.Comment: 10 page

    Market survey of the periwinkle Tympanotonus fuscatus in Rivers State: Sizes, prices, trade routes and exploitation levels

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    Tympanotonus fuscatus was collected from 23 markets through Rivers State (Nigeria), a few in neighbouring states, and from an unexploited population at Buguma. The size distribution of shells was determined,and information on prices and trade routes was also obtained. The mean shell length of specimens from the unexploited Buguma population was 46.4 mm, compared to 30.4 mm for the Buguma market samples. Mean sizes in other markets showed a geographic pattern: the smallest were from the Adoni-Ogoni-Opobo sector (28.1-30.9); the largest were from the Nembe-Brass sector (37.7-44.2) and Bendel State (35.7-45.6); The results suggest the population structure of Tympanotonus in much of Rivers State has been strongly impacted by overharvesting. They show that local market as well as some in Cross River State, are increasingly being supplied by road with specimens from the Benin River area of Bendel State. Differences between shell types; and relations between shell size, selling price and market distance from source, are also discusse

    Monopole clusters in Abelian projected gauge theories

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    We show that the monopole currents which one obtains in the maximally Abelian gauge of SU(2) fall into two quite distinct classes (when the volume is large enough). In each field configuration there is precisely one cluster that permeates the whole lattice volume. It has a current density and a magnetic screening mass that scale and it produces the whole of the string tension. The remaining clusters have a number density that follows an approximate power law proportional to the inverse cube of l where l is the length of the monopole world line in lattice units. These clusters are localised in space-time with radii which vary as the square root of l. In terms of the radius r these `lumps' have a scale-invariant distribution proportional to (dr/r . 1/{r^4}). Moreover they appear not to contribute at all to the string tension. The fact that they are scale-invariant at small distances would seem to rule out an instanton origin.Comment: LaTeX, 31 pages, 11 PostScript figures. Typo in Table 2 correcte

    On the Approximation Performance of Fictitious Play in Finite Games

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    We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play fails to find a solution having an additive approximation guarantee significantly better than 1/2. Our construction shows that for n times n games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity 1/2 - O(1/n^(1-delta)) for arbitrarily small delta. We also show an essentially matching upper bound of 1/2 - O(1/n)

    Groups whose locally maximal product-free sets are complete

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    Let G be a finite group and S a subset of G. Then S is product-free if S ∩ SS = ∅, and complete if G∗ ⊆ S ∪ SS. A product-free set is locally maximal if it is not contained in a strictly larger product-free set. If S is product-free and complete then S is locally maximal, but the converse does not necessarily hold. Street and Whitehead [J. Combin. Theory Ser. A 17 (1974), 219–226] defined a group G as filled if every locally maximal product-free set S in G is complete (the term comes from their use of the phrase ‘S fills G’ to mean S is complete). They classified all abelian filled groups, and conjectured that the finite dihedral group of order 2n is not filled when n = 6k +1 (k ≥ 1). The conjecture was disproved by two of the current authors [C.S. Anabanti and S.B. Hart, Australas. J. Combin. 63 (3) (2015), 385–398], where we also classified the filled groups of odd order. In this paper we classify filled dihedral groups, filled nilpotent groups and filled groups of order 2n p where p is an odd prime. We use these results to determine all filled groups of order up to 2000

    POPCORN: a Supervisory Control Simulation for Workload and Performance Research

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    A multi-task simulation of a semi-automatic supervisory control system was developed to provide an environment in which training, operator strategy development, failure detection and resolution, levels of automation, and operator workload can be investigated. The goal was to develop a well-defined, but realistically complex, task that would lend itself to model-based analysis. The name of the task (POPCORN) reflects the visual display that depicts different task elements milling around waiting to be released and pop out to be performed. The operator's task was to complete each of 100 task elements that ere represented by different symbols, by selecting a target task and entering the desired a command. The simulated automatic system then completed the selected function automatically. Highly significant differences in performance, strategy, and rated workload were found as a function of all experimental manipulations (except reward/penalty)
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