Zsolt Katona - Research |
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Click here for my Google Scholar Profile Work in progress / under review
Language Models for Automated Market Research: A New Way to Generate Perceptual Maps Abstract This paper uses generative language models to substitute for human participants in market research. Such AI-based models can be used to generate textual continuation given a prompt. By carefully formulating the prompts, the paper shows that this new method generates perceptual maps that are close to those generated from human surveys. The application includes perceptual maps based on both brand similarity measures and product attribute ratings. The results demonstrate that using this new method of automated market research can reproduce perceptual maps obtained via human surveys, but at much lower cost. Furthermore, this paper shows that AI-based market research can be applied to answer more nuanced questions based on demographic variables or contextual variation that is prohibitively expensive or infeasible with human respondents On the Capital Market Consequences of Alternative Data: Evidence from Outer Space Abstract We study the emergence of satellite imagery of parking lot traffic across major U.S. retailers as a source of alternative data in capital markets. While satellite imagery signals embed timely information for earnings announcements, stock prices do not incorporate this information prior to the public disclosure of retailer performance. This creates opportunities for sophisticated investors to formulate trading strategies at the expense of individual investors, who tend to be on the other side of the trade. The evidence shows that unequal access to alternative data can increase information asymmetry between sophisticated investors and individual investors without necessarily enhancing price discovery. When and How Should Firms Differentiate? Quality, Advertising and Pricing Decisions in a Duopoly Abstract One of the hallmarks of competitive interaction is each firm's desire to differentiate from rivals. Although differentiation may be achieved through product related choices, advertising levels may constitute another key mechanism. In this paper, we examine under what conditions firms will elect to differentiate through product quality vs. advertising intensity and characterize the set of equilibria that emerge. Consumers can only purchase from the set of products they are informed about through advertising, and choose the alternative that maximizes their utility. Firms select product quality in a first stage, advertising levels in a second stage, and prices in the last stage. We study two forms of advertising-blanket and targeted. Under blanket advertising, firms communicate indiscriminately and a consumer's probability of seeing an ad depends on the level of ad expenditure. We find that when advertising is ineffective, i.e., the additional awareness generated by a heavy level is modest relative to the cost, both firms choose a light ad spending. This allows them to minimally differentiate in qualities without concern of intense price competition, as each firm expects to have a segment of 'captive' consumers that are only aware of its product. When advertising is moderately effective, one firm shifts to expending heavily on advertising, hence all consumers are aware of its product. However, the rival prefers to differentiate by advertising lightly, while choosing the same maximal quality level. This strategy softens price competition by inducing the heavy-advertiser to price highly more often in order to capitalize on its captive segment and allows the light-advertiser to increase its average price. Interestingly, we show that even if advertising heavily entails no extra cost, one firm will choose to advertise lightly in equilibrium for strategic reasons. When advertising is very effective, both firms advertise heavily. In this scenario, firms must differentiate in qualities in order to achieve positive profits. Under targeted advertising, we let firms choose the segment(s) they wish to inform. We identify conditions such that both firms choose equally high quality products, but advertise to distinct segments; thereby achieving differentiation through ad targeting. We further show that this can result in a pocket of unserved consumers, even though consumers with lower willingness to pay purchase. Generally speaking, we show that allowing market awareness to be determined endogenously suggests far less product differentiation than previously suspected and reveals regions where advertising creates viable differentiation. Keywords: Product Quality, Advertising Strategy, Differentiation, Competition agents Ad Blocking Abstract In recent years, ad blocking has become a significant threat to advertising supported publishers. Adblockers typically negotiate with publishers, allowing some ads to go through in return for a payment, a practice called "whitelisting'' in the industry. This paper builds an analytic model to explore the strategic interaction between publishers and adblockers to assess the effect of ad blocking on publishers' quality choices, consumer surplus and total welfare. In a setup with a single publisher and an adblocker that has full negotiating power, we find that the impact of ad blocking critically depends on the extent of consumer heterogeneity in the valuation of quality and sensitivity to advertising. Ad blocking harms publishers and unless consumer heterogeneity is minimal in both dimensions it harms total consumer surplus as well. While some consumers are always better off in the presence of ad blocking, content quality declines and this negative effect on the average consumer is typically not compensated by the positive impact of reduced ad exposure. We explore the impact of varying levels of negotiation power between adblocker and publisher to find that, full negotiation power is not preferred by the adblocker. We then extend our analysis to multiple publishers with different levels of competition between them. We find that a common adblocker creates a strategic link between the publishers, which can either reinforce or attenuate the effect of ad blocking. Nevertheless, the overall negative effect of ad blocking is confirmed. In the discussion section, we report some robustness checks and further elaborate on a number extensions that are available in additional analyses. In particular, we explore the possibility for publishers to introduce a subscription model and we analyze the problem of a transaction platform (e.g. a social network) that seeks to optimally `regulate' ad blocking for the overall benefit of its diverse user base. Quality Score: The Cost of a Virtuous Cycle Abstract Search engines and many social advertising platforms use the so-called quality score to favor certain advertisers in their advertising auction. While the standard justification for quality scores is the need to provide discounts to advertisers with higher click-through rates, this work examines the role of quality score in enticing heterogeneous advertisers to invest in quality and its impact on ad platforms' revenue. The results suggest that a quality score function that rewards bidders in excess of their click-through rates does increase the quality investments but in a non-monotonic way. Higher rewards of landing page quality do not necessarily mean higher investments. Furthermore, such an improvement in quality levels often comes with a sacrifice of the auction revenue despite the higher bids. While the potential revenue impact for the auctioneer depends on the bidding strategies and auction formats, there exists a quality score function that ensures increased revenues by rewarding quality improvement. Several managerial implications for both advertisers and publishers are discussed. Shopping or Dining? Analyzing User Behavior due to Flight Delays Abstract Flight delays are costly to passengers, the air travel industry, businesses, and the overall economy. Yet, there is little empirical evidence on how passengers behave and spend their time as a result of given time due to schedule disruptions. In this study, we use a large proprietary dataset on passengers' indoor movements from a major airport and publicly available flight delay data to study how flyers spend their time due to flight delays. We find that, on average, for every ten minutes of delay, passengers spend twenty additional seconds near shops and 8 seconds near dining establishments. Furthermore, we find that passengers at lower rated airlines are more likely to spend time at dining establishment. Our findings can aid airlines and airports to better manage passengers satisfaction due to service disruptions. Real or Fake: Managing User Authenticity in Ad Auctions Abstract This paper examines the role of fake user activity in online advertising. Publishers and advertisers can be hurt by user actions that are not authentic, especially if they result in advertising events that are paid for. For example, many advertisers on Facebook complain of fake likes that they pay for, but do not get any value out of. The paper models online advertising as a common value auction, where each advertiser gets a private signal about the likelihood of the authenticity of the user reached through advertising. The auction exhibits winner's curse as advertisers who believe the proportion of authentic user activity to be higher also bid higher. Due to the second price auctions typically used in online advertising this leads to a higher price paid only if there are many bidders with concentrated valuations. In this case, the publisher benefits from fake user activity. In settings with few bidders with dispersed valuations the advertisers benefit from the uncertainty about the fake activity and the publisher suffers. The paper also examines when and how should the publisher defend against fake activity. The results show that defending by blocking user accounts based on activity patterns can backfire, because fake users will mimic legitimate user activities and interfere with advertising more. Competing for Influencers in a Social Network Abstract This paper studies the competition between firms for influencers in a network. Firms spend effort to convince influencers to recommend their products. The analysis identifies the offensive and defensive roles of spendgin on influencers. The value of an influencer only depends on the in-degree distribution of the influence network. Influencers who exclusively cover a high number of consumers are more valuable to firms than those who mostly cover consumers also covered by other influencers. Firm profits are highest when there are many consumers with a very low or with very high in-degree. Consumers with an intermediate level of in-degree contribute negatively to profits and high in-degree consumers increase profits when market competition is not intense. Prices are generally lower when consumers are covered by many influencers, however, firms are not always worse off with lower prices. The nature of consumer response to recommendations makes an important difference. When first impressions dominate, firm profits for dense networks are higher, but when recommendations have a cumulative influence profits are reduced as the network becomes dense. Agenda Chasing and Contests Among News Providers Abstract We model competition among news providers as a contest where each firm chooses to publish on a topic from a large pool of topics with different prior success probabilities. If a topic is successful, firms that chose to publish on it share a fixed reward. We explore how increased competition (as measured by the number of firms and/or the share-structure of the reward) and the prior distribution of topics affect the diversity of published news. We relate our findings to current trends in news media, characterized by lower barriers to entry and the increased use of sophisticated technologies to identify successful topics from the large amount of, both professional and user-generated content available on the Internet. We show that the contest nature of competition tends to lead to a broader set of published media themes with a higher representation for marginal topics. The breadth of topics increases the more topics follow a ``fat-tail'' prior distribution and the more a priori popular topics' success are correlated. It also increases with the number of competing firms but only if the share of the reward in the contest dissipates rapidly. We also explore the effect of asymmetry on competition. First, we assume that some firms have a `brand', i.e. a capability to attract a loyal audience. We show that branded publishers are more likely to choose topics with high prior success probabilities, while unbranded publishers tend to choose a priori `unlikely' topics. Second, we assume that some firms have better forecasting capability for the topics' success. Surprisingly, in this case, less informed firms choose topics in a conservative way (i.e. publish topics with the highest prior probabilities). When many firms reporting on the same topic increases the topic's rate of success, marginal topics may emerge but only if the contest is not too competitive and competing firms are neither too few nor too numerous. These findings are related to current trends in the news media industry. Democracy in Product Design: Consumer Participation and Differentiation Strategies Abstract An increasing number of firms use social media to allow their customers to vote on new product design. This paper studies the implications of employing such a democratic product design (DPD). A linear city model is used with random locations to capture uncertainty about consumer preferences and to study strategic forces in monopoly and duopoly settings. The results indicate that a monopolist will use market research to resolve the demand uncertainty, unless DPD provides a cost advantage. In duopoly, an asymmetric equilibrium emerges with exactly only one firm using DPD. Commitment to following consumer votes proves to be a strategic advantage, therefore at least one firm promises not to deviate from the product design consumers voted for. One firm would even self-impose a penalty in order to prevent future deviations. Firm profits are generally hurt by the use of DPD. The role of strategic consumer participation in voting is also explored. The results show that a monopolist prefers an intermediate level of participation cost to ensure an optimal product. In contrast, duopolists are best off when participation costs are very low or very high, because this allows them to avoid using DPD. Contextual Advertising Abstract This paper studies the strategic aspects of contextual advertising. Such advertising entails the display of relevant ads based on the topic of the content a consumer views and takes advantage of the possibility that consumers' content browsing preferences are indicative of their product preferences. The results show that contextual targeting impacts advertiser profit in two ways: first, advertising through relevant content topics helps advertisers reach consumers who have strong preferences for their products. Second, heterogeneity in consumers' content preferences can be leveraged to reduce product market competition, even when consumers are homogeneous in their product preferences. The contextual advertising intermediary's incentives to strategically design its content structure and the targeting precision are governed by the following forces. When product market competition is high, the intermediary offers homogeneous content and increases its targeting precision. This encourages each advertiser to bid for multiple keywords to preventing its competitors from advertising to the consumers. This may lead to an asymmetric equilibrium where one advertiser monopolizes all the advertising spaces to completely preempt competition. When product market competition is low, the intermediary offers heterogeneous content but intentionally decrease its targeting precision. This encourages each advertiser to bid for multiple advertising spaces in order to reach consumers who prefer its product. Media, Aggregators and the Link Economy: Strategic Hyperlink Formation in Content Networks Abstract A key property of the World Wide Web is the possibility for firms to place virtually costless links to third-party content as a substitute or complement to their own content. This ability to hyperlink has enabled new types of players, such as search engines and content aggregators, to successfully enter content ecosystems, attracting traffic and revenues by hosting links to the content of others. This, in turn, has sparked a heated controversy between content producers and aggregators regarding the legitimacy and social costs/benefits of uninhibited free linking. This work is the first to model the implications of interrelated and strategic hyper-linking and content investments. Our results provide a nuanced view of the much-touted "link economy", highlighting both the beneficial consequences and the drawbacks of free hyperlinks for content producers and consumers. We show that content sites can reduce competition and improve profits by forming links to each other; in such networks one site makes high investments in content and other sites link to it. Interestingly, competitive dynamics often preclude the formation of link networks, even in settings where they would improve everyone's profits. Furthermore, such networks improve economic efficiency only when all members have similar abilities to produce content; otherwise the less capable nodes can free-ride on the content of the more capable nodes, reducing profits for the capable nodes as well as the average content quality available to consumers. Within these networks, aggregators have both positive and negative effects. By making it easier for consumers to access good quality content they increase the appeal of the entire content ecosystem relative to the alternatives. To the extent that this increases the total traffic flowing into the content ecosystem, aggregators can help increase the profits of the highest quality content sites. At the same time, however, the market entry of aggregators takes away some of the revenue that would otherwise go to pure content sites. Finally, by placing links to only a subset of available content, aggregators further increase competitive pressure on content sites. Interestingly, this can increase the likelihood that such sites will then attempt to alleviate the competitive pressure by forming link networks. The Race for Sponsored Links: Bidding Patterns for Search Advertising Abstract Web sites invest significant resources in trying to influence their visibility among online search results. In addition to paying for sponsored links, they invest in methods known as search engine optimization (SEO) that improve the ranking of a site among the search results without improving its quality. We study the economic incentives of Web sites to invest in SEO and its implications on search engine and advertiser payoffs. We find that the process is equivalent to an all-pay auction with noise and headstarts. Our results show that, under certain conditions, a positive level of search engine optimization improves the search engine's ranking quality and thus the satisfaction of its visitors. In particular, if the quality of sites coincides with their valuation for visitors then search engine optimization serves as a mechanism that improves the ranking by correcting measurement errors. While this benefits consumers and increases traffic to the search engine, sites participating in search engine optimization could be worse off due to wasteful spending unless their valuation for traffic is very high. We also investigate how search engine optimization affects the revenues from sponsored links. Surprisingly, we find that in many cases search engine revenues are increased by SEO. Network Formation and the Structure of the Commercial World Wide Web Abstract We model the commercial World Wide Web (WWW) as a directed graph emerging as the equilibrium of a game in which utility maximizing Web sites purchase (advertising) in-links from each other, while also setting the price of these links. A key feature of our model is that we consider sites to be heterogeneous in terms of their ``content", i.e. their inherent value to consumers. In a world where consumers `surf' on the WWW, sites' revenues/profits originate from two sources: (i) the sales of content (products) to consumers, and (ii) the sales of links (traffic) to other sites. We find that in equilibrium, higher content sites tend to purchase more advertising links mirroring the Dorfman-Steiner rule. Sites with higher content sell less advertising links and offer such links at higher prices. As such, there seems to be specialization across sites in terms of revenue models: high content sites tend to earns revenue from the sales of content while low content ones from the sales of traffic (advertising), a tendency that is increasing with the size of the browsing population. In an extension, we also allow sites to establish (reference) out-links to each other beyond the sales of advertising links and find that there is a general tendency to establish reference link to sites with higher content. Overall, there is a strong positive correlation between a site's content and the number of its in-links. We also explore network formation in the presence of search engines and find that the higher the proportion of people using these, the more sites have an incentive to specialize in certain ``content areas". Our results have interesting practical implications for `search-engine optimization', the pricing of Internet advertising as well as the choice of Internet business models. They also shed light on why successful search engines (e.g. Google) can use simple heuristics based on in-links to rank sites with respect to their content. Keywords: random graphs, game theory, heterogenous agents Network Effects and Personal Influences: Diffusion of an Online Social Network Abstract We study word-of-mouth effects on the growth of social networks. Aggregate diffusion models ignore the possibility that an individual who is connected to many others in a social network may have a higher adoption probability (degree effect). Furthermore, the density of connections in a group of already adopted consumers may also affect the adoption of individuals connected to this group (clustering effect). We analyze data from one social network for which we know the individual connections between every pair of members. The results support the existence of both degree and clustering effects. We also show how a linear degree effect at the individual level can be the underlying determinant of the Bass model. Furthermore, we present a new methodology to determine the influential power of every individual. Surprisingly, we find that highly connected individuals have a lower average influential power (average influence on a particular person). However, the results suggest that the large number of connections counterbalances the small average influential power, such that highly connected individuals have a higher total influence than their less connected counterparts. We also find evidence that gender and age affect influential power. Keywords: Social Networks, New Product Diffusion The Role of Search Engine Optimization in Search Rankings Abstract Web sites invest significant resources in trying to influence their visibility in online search results. We study the economic incentives of Web sites to invest in this process known as search engine optimization. We focus on methods that improve sites' ranking among the search results without affecting their quality. We find that the process is equivalent to an all-pay auction with noise and headstarts. Our results show that in equilibrium, under certain conditions, some positive level of search engine optimization improves the search engine's ranking and thus the satisfaction of its visitors. In particular, if the quality of sites coincides with their valuation for visitors then search engine optimization serves as a mechanism that improves the ranking by correcting measurement errors. While this benefits consumers and search engines, sites participating in search engine optimization could be worse off unless their valuation for traffic is very high. We also investigate how search engine optimization affects sites' investment in content and find that it can lead to underinvestment as a result of wasteful spending on search engine optimization. Keywords: Search engine marketing, All-pay auctions Competing for Attention in Social Communication Markets Abstract We investigate agents' incentives to communicate with their peers in the context of the emergence of new social media technologies. In particular, we examine the effects of different types of communication cost structures through which new technologies change the way agents send and receive messages. These new social networking technologies make it possible to send the same message to many receivers for the same fixed cost and for negligible (often zero) marginal cost. This is distinct from traditional word-of-mouth which involves additional marginal cost for each intended recipient. Our results show that the new social networking technologies may reduce incentives of some individuals to send messages leading to less diverse communication. As the marginal cost of sending messages to additional people goes down, senders target more receivers leading to higher levels of competition for attention between receivers. The intensified competition requires higher effort on senders' part leading to lower payoffs and, eventually, fewer senders in the population. Although receivers are targeted by more senders and costs go down and they have access to a higher variety of messages, the variety of messages sent by the population decreases. We also study the role of location and horizontal preferences and examine sender differentiation. Endogenous Homophily in Social Networks Abstract It is well known that in most social networks neighbors tend to be similar to each other. Previous research attributed this phenomenon to homophily, that is, that individuals like to connect to others that are similar to them. This paper proposes a network formation model in which individuals can change their location to become more similar before linking to each other to benefit more from the connection. An equilibrium is the outcome describing both the locations and the network resulting in an endogenously formed network with endogenous locations. The results show that the equilibrium network exhibits more homophily than a benchmark with fixed node locations and the number of links increases as link formation costs go down. As costs of changing one's location decrease the network becomes more clustered, less connected and denser. The results explain how certain individuals become opinion leaders throughout this process. The paper also provides a framework that generalizes homophily to examine vertical spaces in addition to horizontal ones. In a horizontal space the distance between two nodes determines how much they benefit from the link, whereas in a vertical space linking to a node with a higher vertical attribute provides more benefits. Keywords: Social networks, Homphily, Network formation Information Communities: The Network Structure of Communication Abstract This study puts forward a variable clique overlap model for identifying information communities, or potentially overlapping subgroups of network actors among whom reinforced independent links ensure efficient communication. We posit that the intensity of communication between individuals in information communities is greater than in other areas of the network. Empirical tests show that the variable clique overlap model is more useful for identifying groups of individuals that have strong internal relationships in closed networks than those defined by more general models of network closure. These findings extend the scope of network closure effects proposed by other researchers working with communication networks using social network methods and approaches, a tradition which emphasizes ties between organizations, groups, individuals, and the external environment. Keywords: Communities, Social networks; Communication; Network closure Bricks and Clicks: The Impact of Product Returns on the Strategies of Multi-Channel Retailers Abstract The Internet has increased the flexibility of retailers allowing them to operate an online arm in addition to their physical stores. While the online channel offers retailers potential advantages in selling to customer segments that value the conveniences of online shopping, it also raises new challenges. These include the higher likelihood of costly product returns when customers' ability to 'touch and feel' the product is important in determining fit. We study competing retailers operating dual channels ("Bricks and Clicks") and examine how pricing strategies and the level of physical store assistance change as a result of the additional Internet outlet. On the supply-side, firms endogenously determine prices and how much to invest in store characteristics that assist customers in finding matching products (e.g., greater shelf display capacity, more qualified staff, floor samples). On the demand-side, we capture two relevant sources of customer heterogeneity: (i) retailer preference, and (ii) shopping trip costs. A central result we obtain is that when differentiation among retailers is not too high, having an online channel actually increases (costly) investment in store assistance levels while prices are set higher. We also examine how firms' range of product categories can vary between the two channels. Our main finding here is that even though it is costless to offer products online, retailers will sell only a limited assortment over the Internet. In particular, only "safe" products with a low chance of being returned will be sold online, while retailers' full range of products will be sold in physical stores. Keywords: Channels of Distribution, Retailing, Internet Marketing, Pricing, Reverse Logistics, Product Returns CAM: A Spreading Activation Network Model of Subcategory Construction Abstract A large body of research suggests that people process the entities that they encounter by placing them into mental categories (Barsalou 1992). Although previous research examines how people access information in hierarchical category structures, it does not examine how people construct individual new categories and, in particular, how the locus of these new categories may depend on the structure of the entire hierarchy. We describe this latter process with a spreading activation model of hierarchical category structures that we call the Category Activation Model (CAM). In an experiment and an empirical study, we show that the CAM reliably predicts the probability that a person will construct a new category at a specific location within a category structure, and we provide evidence that accessibility is the mechanism that underlies category construction. Keywords: random graphs, game theory, heterogenous agents A new class of scale-free graphs Abstract Consider the following modification of the Barab\'asi--Albert random graph. At every step a new vertex is added to the graph. It is connected to the old vertices randomly, with probabilities proportional to the degree of the other vertex, and independently of each other. We show that the proportion of vertices of degree $k$ decreases at the rate of $k^{-3}$. Furthermore, we prove a strong law of large numbers for the maximum degree. Keywords: random graph, scale-free disribution Levels of a scale-free tree Abstract Consider the random graph model of Barabási and Albert, where we add a new vertex in every step and connect it to some old vertices with probabilities proportional to their degrees. If we connect it to only one of the old vertices the graph will be a tree. These graphs have been shown to have power law degree distributions, the same as observed in some large real-world networks. We show that the degree distribution is the same on every sufficiently high level of the tree.AMS classification: 05C80, 60C05 Keywords: random graphs, scale-free disribution, width of trees Width of a scale-free tree Abstract Consider the random graph model of Barabási and Albert, where we add a new vertex in every step and connect it to some old vertices with probabilities proportional to their degrees. If we connect it to only one of the old vertices this will be a tree. These graphs have been shown to have a power law degree distribution, the same as obsereved in some large real-world networks. We are interested in the width of the tree and show that it is W(n) ~ n/sqrt(Pi log n) and this also holds for a slight generalization of the model with another constant. Then we see how this theoretical result can be applied to directory trees.AMS classification: 05C80, 60C05 Keywords: random graphs, scale-free disribution, width of trees 3-wise exactly 1-intersecting families of sets Abstract Let f(l,t,n) be the maximal size of a family F a subset of 2[n] such that any l at least 2 sets of F have an exactly t-element intersection. If l is at least 3, it trivially comes from a paper of Füredi that the optimal families are trivially intersecting (there is a t-element core contained by all the members of the family). Hence it is easy to determine f(l,t,n)=[(t/2)(n-1)]+1. Let g(l,t,n) be the maximal size of an l-wise exaclty t-intersecting family that is not trivially t-intersecting. We give upper and lower bounds which only meet in the following case: g(3,1,n)=n2/3(1+o(1)).AMS classification: 05D05; 05B25 Keywords: extremal problems for families of finite sets; finite projective geometries Multiply intersecting families of sets (with Zoltán Füredi) Abstract Let [n] denote the set {1,2,...,n}, 2[n] the collection of all subsets of [n] and F a subset of 2[n] be a family. The maximum of |F| is studied if any r subsets have an at least s-element intersection and there are no l subsets containing t+1 common elements. We show that |F| is at most \sum_{i=0}^{t-s} \binom{n-s}{i}+ \frac{t+\ell-s}{t+2-s}\binom{n-s}{t+1-s}+\min\{s-1, l-2\} and this bound is asymptotically the best possible as n goes to infinty and t is at least 2s is at least 2, and r,l that are at least 2 are fixed.AMS classification: 05D05; 05B25 Keywords: extremal problems for families of finite sets Intersecting families of sets, no l containing two common elements Abstract Let H denote the set {f1,f2,...,fn}, 2[n] the collection of all subsets of H and F a subset of 2[n] be a family. The maximum of |F| is studied if any k subsets have a non-empty intersection and the intersection of any l distinct subsets (1<=k<l) is empty. This problem is reduced to a covering problem.AMS classification: 05D05; 05B25 Keywords: extremal problems for families of finite sets; finite projective geometries |
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