Csec

Adoption or rejection of ideas, products, and technologies in a society is often governed by simultaneous propagation of positive and negative influences. Consider a planner trying to introduce an idea in different parts of a society at different times. How should the planner design a schedule considering this fact that positive reaction to the idea in early areas has a positive impact on probability of success in later areas, whereas a flopped reaction has exactly the opposite impact? We generalize a well-known economic model which has been recently used by Chierichetti, Kleinberg, and Panconesi (ACM EC'12). In this model the reaction of each area is determined by its initial preference and the reaction of early areas. We model the society by a graph where each node represents a group of people with the same preferences. We consider a full propagation setting where news and influences propagate between every two areas. We generalize previous works by studying the problem when people in different areas have various behaviors. We first prove, independent of the planner's schedule, influences help (resp., hurt) the planner to propagate her idea if it is an appealing (resp., unappealing) idea. We also study the problem of designing the optimal non-adaptive spreading strategy. In the non-adaptive spreading strategy, the schedule is fixed at the beginning and is never changed. Whereas, in adaptive spreading strategy the planner decides about the next move based on the current state of the cascade. We demonstrate that it is hard to propose a non-adaptive spreading strategy in general. Nevertheless, we propose an algorithm to find the best non-adaptive spreading strategy when probabilities of different behaviors of people in various areas drawn i.i.d from an unknown distribution. Then, we consider the influence propagation phenomenon when the underlying influence network can be any arbitrary graph. We show it is #P-complete to compute the expected number of adopters for a given spreading strategy. However, we design a polynomial-time algorithm for the problem of computing the expected number of adopters for a given schedule in the full propagation setting. Last but not least, we give a polynomial-time algorithm for designing an optimal adaptive spreading strategy in the full propagation setting.

is a fundamental economic model that represents firms competing in a single market of a homogeneous good. Each firm tries to maximize its utility-naturally a function of the production cost as well as market price of the product-by deciding on the amount of production. This problem has been studied comprehensively in Economics and Game Theory; however, in today's dynamic and diverse economy, many firms often compete in more than one market simultaneously, i.e., each market might be shared among a subset of these firms. In this situation, a bipartite graph models the access restriction where firms are on one side, markets are on the other side, and edges demonstrate whether a firm has access to a market or not. We call this game Network Cournot Competition (NCC). Computation of equilibrium, taking into account a network of markets and firms and the different forms of cost and price functions, makes challenging and interesting new problems. In this paper, we propose algorithms for finding pure Nash equilibria of NCC games in different situations. First, we carefully design a potential function for NCC, when the price functions for markets are linear functions of the production in that market. This result lets us leverage optimization techniques for a single function rather than multiple utility functions of many firms. However, for nonlinear price functions, this approach is not feasible-there is indeed no single potential function that captures the utilities of all firms for the case of nonlinear price functions. We model the problem as a nonlinear complementarity problem in this case, and design a polynomial-time algorithm that finds an equilibrium of the game for strongly convex cost functions and strongly monotone revenue functions. We also explore the class of price functions that ensures strong monotonicity of the revenue function, and show it consists of a broad class of functions. Moreover, we discuss the uniqueness of equilibria in both of these cases which means our algorithms find the unique equilibria of the games. Last but not least, when the cost of production in one market is independent from the cost of production in other markets for all firms, the problem can be separated into several independent classical Cournot Oligopoly problems in which the firms compete over a single market. We give the first combinatorial algorithm for this widely studied problem. Interestingly, our algorithm is much simpler and faster than previous optimization-based approaches.

We study the power of fractional allocations of resources to maximize our influence in a network. This work extends in a natural way the well-studied model by Kempe, Kleinberg, and Tardos (2003), where a designer selects a (small) seed set of nodes in a social network to influence directly, this influence cascades when other nodes reach certain thresholds of neighbor influence, and the goal is to maximize the final number of influenced nodes. Despite extensive study from both practical and theoretical viewpoints, this model limits the designer to a binary choice for each node, with no chance to apply intermediate levels of influence. This model captures some settings precisely, such as exposure to an idea or pathogen, but it fails to capture very relevant concerns in others, for example, a manufacturer promoting a new product by distributing five "20% off" coupons instead of giving away a single free product. While fractional versions of problems tend to be easier to solve than integral versions, for influence maximization, we show that the two versions have essentially the same computational complexity. On the other hand, the two versions can have vastly different solutions: the added flexibility of fractional allocation can lead to significantly improved influence. Our main theoretical contribution is to show how to adapt the major positive results from the integral case to the fractional case. Specifically, Mossel and Roch (2006) used the submodularity of influence to obtain their integral results; we introduce a new notion of continuous submodularity, and use this to obtain matching fractional results. We conclude that we can achieve the same greedy (1 − 1/e − ε)-approximation for the fractional case as the integral case, and that other heuristics are likely to carry over as well. In practice, we find that the fractional model performs substantially better than the integral model, according to simulations on real-world social network data.

Title of dissertation: COMPUTATIONAL ANALYSIS OF INTELLIGENT AGENTS: SOCIAL AND STRATEGIC SETTINGS Anshul Sawant, Doctor of Philosophy, 2016 Dissertation co-directed by: Prof. V.S. Subrahmanian, Department of Computer Science Prof. Mohammad Taghi. Hajiaghayi, Department of Computer Science The central motif of this work is prediction and optimization in presence of multiple interacting intelligent agents. We use the phrase ‘intelligent agents’ to imply in some sense, a ‘bounded rationality’, the exact meaning of which varies depending on the setting. Our agents may not be ‘rational’ in the classical game theoretic sense, in that they don’t always optimize a global objective. Rather, they rely on heuristics, as is natural for human agents or even software agents operating in the real-world. Within this broad framework we study the problem of influence maximization in social networks where behavior of agents is myopic, but complication stems from the structure of interaction networks....

The use of game theory to model conflict has been studied by several researchers, spearheaded by Schelling [1960]. Most of these efforts assume a single payoff matrix that captures players’ utilities under different assumptions about what the players will do. Our experience in counter-terrorism applications is that experts disagree on these payoffs. We leverage Shapley’s [1959] notion of vector equilibria, which formulates games where there are multiple payoff matrices, but note that they are very hard to compute in practice. In order to effectively enumerate large numbers of equilibria with payoffs provided by multiple experts, we propose a novel combination of vector payoffs and well-supported -approximate equilibria [Daskalakis et al. 2006b]. We develop bounds related to computation of these equilibria for some special cases, and give a quasi-polynomial time approximation scheme (QPTAS) for the general case when the number of players is small (which is true in many real-world app...

A metric space is often represented as the pair (X,d). An example of metric spaces is (R, Lk), where Lk is the k-norm over R for given n, k ∈ Z≥1. We can represent a finite metric space (X, d) by a symmetric matrix S, of size nxn, where Si,j = d(i, j) and |X| = n. Metric spaces can be visualized using undirected graph G, where S is distance matrix for G. Conversely, given a graph G(V, E), we can represent it as a metric space (V, d), where d(i, j) is length of the shortest path between i, j ∈ V.

Deadline-TSP (DTSP) and Vehicle routing with time-windows (VRTW) are extensions of the much studied TSP problem where each vertex to be visited has a time-window associated with it and server is rewarded only if it visits a node during this time window. For the deadline-TSP problem, all release

Determining complementarity between products when viewing products online, e.g., via a shopping website or a search engine, is not straightforward. The information required to determine product complementarity is unstructured and/or spread across multiple sources. While co-purchase data can be used to infer complementarity, this requires large volumes of purchase data that is often unavailable. This disclosure describes techniques to identify relationships between products based on analysis of web search queries, subsequent clicks or other user actions, obtained with user permission. The techniques rely on the observation that query streams often include searches for related products, e.g., in the form of “A for B” queries (or queries in other forms) when searching for a product A compatible with a product B. Entity extraction is performed on such query streams and a machine learning model is utilized to identify likely complementary products

is a fundamental economic model that represents firms competing in a single market of a homogeneous good. Each firm tries to maximize its utility-naturally a function of the production cost as well as market price of the product-by deciding on the amount of production. This problem has been studied comprehensively in Economics and Game Theory; however, in today's dynamic and diverse economy, many firms often compete in more than one market simultaneously, i.e., each market might be shared among a subset of these firms. In this situation, a bipartite graph models the access restriction where firms are on one side, markets are on the other side, and edges demonstrate whether a firm has access to a market or not. We call this game Network Cournot Competition (NCC). Computation of equilibrium, taking into account a network of markets and firms and the different forms of cost and price functions, makes challenging and interesting new problems. In this paper, we propose algorithms for finding pure Nash equilibria of NCC games in different situations. First, we carefully design a potential function for NCC, when the price functions for markets are linear functions of the production in that market. This result lets us leverage optimization techniques for a single function rather than multiple utility functions of many firms. However, for nonlinear price functions, this approach is not feasible-there is indeed no single potential function that captures the utilities of all firms for the case of nonlinear price functions. We model the problem as a nonlinear complementarity problem in this case, and design a polynomial-time algorithm that finds an equilibrium of the game for strongly convex cost functions and strongly monotone revenue functions. We also explore the class of price functions that ensures strong monotonicity of the revenue function, and show it consists of a broad class of functions. Moreover, we discuss the uniqueness of equilibria in both of these cases which means our algorithms find the unique equilibria of the games. Last but not least, when the cost of production in one market is independent from the cost of production in other markets for all firms, the problem can be separated into several independent classical Cournot Oligopoly problems in which the firms compete over a single market. We give the first combinatorial algorithm for this widely studied problem. Interestingly, our algorithm is much simpler and faster than previous optimization-based approaches.