In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.

A: Shortest path distance in random k-nearest neighbor graphs
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Q: We introduce a compact graph-theoretic repre­ sentation for multi-party game theory. Our main result is a provably correct and efficient algo­ rithm for computing approximate Nash equilibria in one-stage games represented by trees or sparse graphs.

A: Graphical Models for Game Theory
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Q: In search engines, online marketplaces and other human–computer interfaces large collectives of individuals sequentially interact with numerous alternatives of varying quality. In these contexts, individual trial and error (exploration) is crucial for uncovering novel high-quality items or solutions, but entails a high cost for individual agents [Frazier et al. 2014]. Self-interested decision makers, we will show, are often better off imitating the choices of individuals who have already incurred the costs of exploration. Although imitation makes sense at the individual level, it deprives the group of additional information that could have been gleaned by individual explorers [Rogers 1988]. Under these grim circumstances, certain non-monetary mechanisms can keep imitation forces in check and allow the collective to reap some of the benefits of the independent collection of information. For example, in simultaneous exploration problems, a natural equilibrium evolves between explorers and imitators [Conlisk 1980; Kameda and Nakanishi 2002]. Further, in some collective exploration settings, barriers to communication such as a sparser communication network among individuals can prove beneficial at the collective level. They encourage people to explore more, thus supplying useful information to the group [Fang et al. 2010; Lazer and Friedman 2007; Mason et al. 2008; Toyokawa et al. 2014]. Diversity is known to be a blessing for groups and collectives, as they can leverage the wealth of information possessed by different individuals [Conradt et al. 2013; Davis-Stober et al. 2014; MüllerTrede et al. 2017] or take advantage of the complementarities between group members to solve complex problems [Clearwater et al. 1991; Hong and Page 2004]. Could some preference diversity be beneficial in problems where collectives sequentially explore numerous alternatives, and thus despite reducing the immediate value of social learning lead to an increase in collective welfare?

A:
Diversity of preferences can increase collective welfare in sequential exploration problems
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