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We study a game where agents interacting over a network engage in two coupled activities and have to strategically decide their production for each of these activities. Agent interactions involve local and global network effects, as well as a coupling between activities. We consider the general case where the network effects are heterogeneous across activities, i.e., the underlying graph structures of the two activities differ and/or the parameters of the network effects are not equal. In particular, we apply this game in the context of palm oil tree cultivation and timber harvesting, where network structures are defined by spatial boundaries of concessions. We first derive a sufficient condition for the existence and uniqueness of a Nash equilibrium. This condition can be derived using the potential game property of our game or by employing variational inequality framework. We show that the equilibrium can be expressed as a linear combination of two Bonacich centrality vectors. 

This article studies a problem of strategic network inspection, in which a defender (agency) is tasked with detecting the presence of multiple attacks in the network. An inspection strategy entails monitoring the network components, possibly in a randomized manner, using a given number of detectors. We formulate the network inspection problem [Formula: see text] as a large-scale bilevel optimization problem, in which the defender seeks to determine an inspection strategy with minimum number of detectors that ensures a target expected detection rate under worst-case attacks. We show that optimal solutions of [Formula: see text] can be obtained from the equilibria of a large-scale zero-sum game. Our equilibrium analysis involves both game-theoretic and combinatorial arguments and leads to a computationally tractable approach to solve [Formula: see text]. First, we construct an approximate solution by using solutions of minimum set cover (MSC) and maximum set packing (MSP) problems and evaluate its detection performance. In fact, this construction generalizes some of the known results in network security games. Second, we leverage properties of the optimal detection rate to iteratively refine our MSC/MSP-based solution through a column generation procedure. Computational results on benchmark water networks demonstrate the scalability, performance, and operational feasibility of our approach. The results indicate that utilities can achieve a high level of protection in large-scale networks by strategically positioning a small number of detectors. 

This article poses the following problem: Does there exist a probability distribution over subsets of a finite partially ordered set (poset), such that a set of constraints involving marginal probabilities of the poset’s elements and maximal chains is satisfied? We present a combinatorial algorithm to positively resolve this question. The algorithm can be implemented in polynomial time in the special case where maximal chain probabilities are affine functions of their elements. This existence problem is relevant for the equilibrium characterization of a generic strategic interdiction game on a capacitated flow network. The game involves a routing entity that sends its flow through the network while facing path transportation costs and an interdictor who simultaneously interdicts one or more edges while facing edge interdiction costs. Using our existence result on posets and strict complementary slackness in linear programming, we show that the Nash equilibria of this game can be fully described using primal and dual solutions of a minimum-cost circulation problem. Our analysis provides a new characterization of the critical components in the interdiction game. It also leads to a polynomial-time approach for equilibrium computation. 

This article presents an azimuthally asymmetric gradient hurricane wind field model that can be coupled with hurricane-track models for engineering wind risk assessments. The model incorporates low-wavenumber asymmetries into the maximum wind intensity parameter of the Holland et al. wind field model. The amplitudes and phases of the asymmetries are parametric functions of the storm-translation speed and wind shear. Model parameters are estimated by solving a constrained, nonlinear least squares (CNLS) problem that minimizes the sum of squared residuals between wind field intensities of historical storms and model-estimated winds. There are statistically significant wavenumber-1 asymmetries in the wind field resulting from both storm translation and wind shear. Adding the translation vector to the wind field model with wavenumber-1 asymmetries further improves the model’s estimation performance. In addition, inclusion of the wavenumber-1 asymmetry resulting from translation results in a greater decrease in modeling error than does inclusion of the wavenumber-1 shear-induced asymmetry. Overall, the CNLS estimation method can handle the inherently nonlinear wind field model in a flexible manner; thus, it is well suited to capture the radial variability in the hurricane wind field’s asymmetry. The article concludes with brief remarks on how the CNLS-estimated model can be applied for simulating wind fields in a statistically generated ensemble.