Competitive Foods

Describes the types of food items available to middle and high school students in forty California public secondary schools, as well as how well they match the nutrient standards defined in California's SB 12 legislation

Competitive Tiling

Competitive tiling consists of two players, a tile set, a region, and a non-negative integer d. Alice and Bob, our two players, alternate placing tiles on the untiled squares of the region. They play until no more tiles can be placed. Alice wins if at most d squares are untiled at the end of the game, and Bob wins if more than d squares are untiled. For given regions and tile sets we are interested in the smallest value of d such that Alice has a winning strategy. We call this the game tiling number. In this project, we focus on finding the game tiling number for the game played with dominoes on 2 x n rectangles, modified 2 x n rectangles, and rectangular annular regions

Competitive Priorities and Competitive Advantage in Jordanian Manufacturing

The purpose of this research was to explore and predict the relationship between the competitive priorities (quality, cost, flexibility and delivery) and the competitive advantage of firms in the Jordanian Industrial Sector. A population of 88 Jordanian manufacturing firms, registered on the Amman Stock Exchange, was targeted using a cross-sectional survey employing a questionnaire method of data collection. The results of the data analysis indicate a significant relationship between competitive priorities and competitive advantage. The research suggests that recognising and nurturing this relationship provides the master key for a firm to survive in a turbulent environment. Therefore, operational and marketing strategies should place emphasis on competitive priorities such as quality, cost, flexibility and delivery to achieve, develop and maintain competitive advantage. This study is one of the first to examine the relationship between the competitive priorities of Jordanian manufacturing firms and their competitive advantage

Competitive comparison in music: influences upon self-efficacy beliefs by gender

This study profiles gender differences in instrumental performance self-efficacy perceptions of high school students (N = 87) over the course of a three-day orchestra festival in which students competed against one another for rank-based seating and then rehearsed and performed as a group. Reported self-beliefs rose significantly for the sample over the course of the festival. Self-efficacy beliefs of females were significantly lower than those of males before the seating audition and first rehearsal, but were no longer different by the midpoint of the festival. Survey free-response data were coded according to Bandura's (1997 Bandura, A. 1997. Self-efficacy: The Exercise of Control. New York: W. H. Freeman.) four sources of self-efficacy. A 52% drop in the frequency of student comments regarding competitive comparison appeared at the same point in which female self-efficacy beliefs were no longer different from those of males. Results support past research to suggest that males and females may respond differently to rank-based competition versus social support

Competitive Pressure: Competitive Dynamics as Reactions to Multiple Rivals

Competitive dynamics research has focused primarily on interactions between dyads of firms. Drawing on the awareness-motivation-capability framework and strategic group theory we extend this by proposing that firms’ actions are influenced by perceived competitive pressure resulting from actions by several rivals. We predict that firms’ action magnitude is influenced by the total number of rival actions accumulating in the market, and that this effect is moderated by strategic group membership. We test this using data on the German mobile telephony market and find them supported: the magnitude of firm’s actions is influenced by a buildup of actions by multiple rivals, and firms react more strongly to strategically similar rivals

Optimal Competitive Auctions

We study the design of truthful auctions for selling identical items in unlimited supply (e.g., digital goods) to n unit demand buyers. This classic problem stands out from profit-maximizing auction design literature as it requires no probabilistic assumptions on buyers' valuations and employs the framework of competitive analysis. Our objective is to optimize the worst-case performance of an auction, measured by the ratio between a given benchmark and revenue generated by the auction. We establish a sufficient and necessary condition that characterizes competitive ratios for all monotone benchmarks. The characterization identifies the worst-case distribution of instances and reveals intrinsic relations between competitive ratios and benchmarks in the competitive analysis. With the characterization at hand, we show optimal competitive auctions for two natural benchmarks. The most well-studied benchmark $\mathcal{F}^{(2)}(\cdot)$ measures the envy-free optimal revenue where at least two buyers win. Goldberg et al. [13] showed a sequence of lower bounds on the competitive ratio for each number of buyers n. They conjectured that all these bounds are tight. We show that optimal competitive auctions match these bounds. Thus, we confirm the conjecture and settle a central open problem in the design of digital goods auctions. As one more application we examine another economically meaningful benchmark, which measures the optimal revenue across all limited-supply Vickrey auctions. We identify the optimal competitive ratios to be $(\frac{n}{n-1})^{n-1}-1$ for each number of buyers n, that is $e-1$ as $n$ approaches infinity

Competitive Gradient Descent

We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash equilibrium of a regularized bilinear local approximation of the underlying game. It avoids oscillatory and divergent behaviors seen in alternating gradient descent. Using numerical experiments and rigorous analysis, we provide a detailed comparison to methods based on \emph{optimism} and \emph{consensus} and show that our method avoids making any unnecessary changes to the gradient dynamics while achieving exponential (local) convergence for (locally) convex-concave zero sum games. Convergence and stability properties of our method are robust to strong interactions between the players, without adapting the stepsize, which is not the case with previous methods. In our numerical experiments on non-convex-concave problems, existing methods are prone to divergence and instability due to their sensitivity to interactions among the players, whereas we never observe divergence of our algorithm. The ability to choose larger stepsizes furthermore allows our algorithm to achieve faster convergence, as measured by the number of model evaluations.Comment: Appeared in NeurIPS 2019. This version corrects an error in theorem 2.2. Source code used for the numerical experiments can be found under http://github.com/f-t-s/CGD. A high-level overview of this work can be found under http://f-t-s.github.io/projects/cgd