Price of Competition and Dueling Games

We study competition in a general framework introduced by Immorlica et al. and answer their main open question. Immorlica et al. considered classic optimization problems in terms of competition and introduced a general class of games called dueling games. They model this competition as a zero-sum game, where two players are competing for a user's satisfaction. In their main and most natural game, the ranking duel, a user requests a webpage by submitting a query and players output an ordering over all possible webpages based on the submitted query. The user tends to choose the ordering which displays her requested webpage in a higher rank. The goal of both players is to maximize the probability that her ordering beats that of her opponent and gets the user's attention. Immorlica et al. show this game directs both players to provide suboptimal search results. However, they leave the following as their main open question: "does competition between algorithms improve or degrade expected performance?" In this paper, we resolve this question for the ranking duel and a more general class of dueling games. More precisely, we study the quality of orderings in a competition between two players. This game is a zero-sum game, and thus any Nash equilibrium of the game can be described by minimax strategies. Let the value of the user for an ordering be a function of the position of her requested item in the corresponding ordering, and the social welfare for an ordering be the expected value of the corresponding ordering for the user. We propose the price of competition which is the ratio of the social welfare for the worst minimax strategy to the social welfare obtained by a social planner. We use this criterion for analyzing the quality of orderings in the ranking duel. We prove the quality of minimax results is surprisingly close to that of the optimum solution

The role of search engine optimization in search marketing

This paper examines the impact of search engine optimization (SEO) on the competition between advertisers for organic and sponsored search results. The results show that a positive level of search engine optimization may improve the search engine's ranking quality and thus the satisfaction of its visitors. In the absence of sponsored links, the organic ranking is improved by SEO if and only if the quality provided by a website is sufficiently positively correlated with its valuation for consumers. In the presence of sponsored links, the results are accentuated and hold regardless of the correlation. When sponsored links serve as a second chance to acquire clicks from the search engine, low-quality websites have a reduced incentive to invest in SEO, giving an advantage to their high-quality counterparts. As a result of the high expected quality on the organic side, consumers begin their search with an organic click. Although SEO can improve consumer welfare and the payoff of high-quality sites, we find that the search engine's revenues are typically lower when advertisers spend more on SEO and thus less on sponsored links. Modeling the impact of the minimum bid set by the search engine reveals an inverse U-shaped relationship between the minimum bid and search engine profits, suggesting an optimal minimum bid that is decreasing in the level of SEO activity. © 2013 INFORMS

Growth and Competition in a Model of Human Capital Accumulation and Research

The aim of this paper is to analyze the relationship between competition and growth in a model of human capital accumulation and research by disentangling the monopolistic mark-up in the intermediate goods sector and the returns to specialization in order to have a better measure of competition. We find that the steady-state output growth rate depends on the parameters describing preferences, human capital accumulation technology and R&D activity. We also show that the relationship between competition and growth is inverse U shaped. This result that seems to be in line this empirical results (Aghion and Gri±th (2005)) is explained by the resource allocation effect.Endogenous growth, Horizontal differentiation, Technological change, Imperfect competition, Human capital

Domain-Type-Guided Refinement Selection Based on Sliced Path Prefixes

Abstraction is a successful technique in software verification, and interpolation on infeasible error paths is a successful approach to automatically detect the right level of abstraction in counterexample-guided abstraction refinement. Because the interpolants have a significant influence on the quality of the abstraction, and thus, the effectiveness of the verification, an algorithm for deriving the best possible interpolants is desirable. We present an analysis-independent technique that makes it possible to extract several alternative sequences of interpolants from one given infeasible error path, if there are several reasons for infeasibility in the error path. We take as input the given infeasible error path and apply a slicing technique to obtain a set of error paths that are more abstract than the original error path but still infeasible, each for a different reason. The (more abstract) constraints of the new paths can be passed to a standard interpolation engine, in order to obtain a set of interpolant sequences, one for each new path. The analysis can then choose from this set of interpolant sequences and select the most appropriate, instead of being bound to the single interpolant sequence that the interpolation engine would normally return. For example, we can select based on domain types of variables in the interpolants, prefer to avoid loop counters, or compare with templates for potential loop invariants, and thus control what kind of information occurs in the abstraction of the program. We implemented the new algorithm in the open-source verification framework CPAchecker and show that our proof-technique-independent approach yields a significant improvement of the effectiveness and efficiency of the verification process.Comment: 10 pages, 5 figures, 1 table, 4 algorithm