Abstract Interpretation of Supermodular Games

Supermodular games find significant applications in a variety of models, especially in operations research and economic applications of noncooperative game theory, and feature pure strategy Nash equilibria characterized as fixed points of multivalued functions on complete lattices. Pure strategy Nash equilibria of supermodular games are here approximated by resorting to the theory of abstract interpretation, a well established and known framework used for designing static analyses of programming languages. This is obtained by extending the theory of abstract interpretation in order to handle approximations of multivalued functions and by providing some methods for abstracting supermodular games, in order to obtain approximate Nash equilibria which are shown to be correct within the abstract interpretation framework

Maximizing Welfare in Social Networks under a Utility Driven Influence Diffusion Model

Motivated by applications such as viral marketing, the problem of influence maximization (IM) has been extensively studied in the literature. The goal is to select a small number of users to adopt an item such that it results in a large cascade of adoptions by others. Existing works have three key limitations. (1) They do not account for economic considerations of a user in buying/adopting items. (2) Most studies on multiple items focus on competition, with complementary items receiving limited attention. (3) For the network owner, maximizing social welfare is important to ensure customer loyalty, which is not addressed in prior work in the IM literature. In this paper, we address all three limitations and propose a novel model called UIC that combines utility-driven item adoption with influence propagation over networks. Focusing on the mutually complementary setting, we formulate the problem of social welfare maximization in this novel setting. We show that while the objective function is neither submodular nor supermodular, surprisingly a simple greedy allocation algorithm achieves a factor of $(1-1/e-\epsilon)$ of the optimum expected social welfare. We develop \textsf{bundleGRD}, a scalable version of this approximation algorithm, and demonstrate, with comprehensive experiments on real and synthetic datasets, that it significantly outperforms all baselines.Comment: 33 page

Demonstration: Economic Analysis and Expert Testimony—Plaintiff\u27s Conference

This article is a demonstration on the use of economic experts. The demonstration is based loosely on Mobil’s attempted take-over of Marathon Oil Company. However, the oil companies involved here are named Major, which is the second largest oil company in the United States, and Olympic, which is the largest supplier to independents. Any resemblance of Major and Olympic to any other firm, entity or person, living or not, is purely coincidental. The demonstration is divided into two parts. The first part is the conference. A conference of plaintiff’s team will be followed by a conference of defendant’s team

Demonstration: Economic Analysis and Expert Testimony—Plaintiff\u27s Conference

This article is a demonstration on the use of economic experts. The demonstration is based loosely on Mobil’s attempted take-over of Marathon Oil Company. However, the oil companies involved here are named Major, which is the second largest oil company in the United States, and Olympic, which is the largest supplier to independents. Any resemblance of Major and Olympic to any other firm, entity or person, living or not, is purely coincidental. The demonstration is divided into two parts. The first part is the conference. A conference of plaintiff’s team will be followed by a conference of defendant’s team

Organizing the innovation process : complementarities in innovation networking

This paper contributes to the developing literature on complementarities in organizational design. We test for the existence of complementarities in the use of external networking between stages of the innovation process in a sample of UK and German manufacturing plants. Our evidence suggests some differences between the UK and Germany in terms of the optimal combination of innovation activities in which to implement external networking. Broadly, there is more evidence of complementarities in the case of Germany, with the exception of the product engineering stage. By contrast, the UK exhibits generally strong evidence of substitutability in external networking in different stages, except between the identification of new products and product design and development stages. These findings suggest that previous studies indicating strong complementarity between internal and external knowledge sources have provided only part of the picture of the strategic dilemmas facing firms

Substitute Valuations: Generation and Structure

Substitute valuations (in some contexts called gross substitute valuations) are prominent in combinatorial auction theory. An algorithm is given in this paper for generating a substitute valuation through Monte Carlo simulation. In addition, the geometry of the set of all substitute valuations for a fixed number of goods K is investigated. The set consists of a union of polyhedrons, and the maximal polyhedrons are identified for K=4. It is shown that the maximum dimension of the maximal polyhedrons increases with K nearly as fast as two to the power K. Consequently, under broad conditions, if a combinatorial algorithm can present an arbitrary substitute valuation given a list of input numbers, the list must grow nearly as fast as two to the power K.Comment: Revision includes more background and explanation

Flows and Decompositions of Games: Harmonic and Potential Games

In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the equilibria of a game, but plays a fundamental role in their efficiency properties, thus decoupling the location of equilibria and their payoff-related properties. Exploiting the properties of the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the properties of potential and harmonic games to "nearby" games. We exemplify this point by showing that the set of approximate equilibria of an arbitrary game can be characterized through the equilibria of its projection onto the set of potential games